•

0 likes•70 views

This is my report on Adjusting PageRank parameters and comparing results (version 1). While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli. Web graphs unaltered are reducible, and thus the rate of convergence of the power-iteration method is the rate at which αk → 0, where α is the damping factor, and k is the iteration count. An estimate of the number of iterations needed to converge to a tolerance τ is logα τ. For τ = 10-6 and α = 0.85, it can take roughly 85 iterations to converge. For α = 0.95, and α = 0.75, with the same tolerance τ = 10-6, it takes roughly 269 and 48 iterations respectively. For τ = 10-9, and τ = 10-3, with the same damping factor α = 0.85, it takes roughly 128 and 43 iterations respectively. Thus, adjusting the damping factor or the tolerance parameters of the PageRank algorithm can have a significant effect on the convergence rate, both in terms of time and iterations. However, especially with the damping factor α, adjustment of the parameter value is a delicate balancing act. For smaller values of α, the convergence is fast, but the link structure of the graph used to determine ranks is less true. Slightly different values for α can produce very different rank vectors. Moreover, as α → 1, convergence slows down drastically, and sensitivity issues begin to surface [langville04].

Report

Share

Report

Share

Download to read offline

Adjusting PageRank parameters and comparing results : REPORT

This document discusses experiments adjusting PageRank algorithm parameters and comparing results. It is found that increasing the damping factor α increases iterations exponentially, while decreasing the tolerance τ decreases iterations exponentially. PageRank with L∞ norm converges fastest on average, followed by L2 norm then L1 norm. The most stable method for comparing relative performance is the geometric mean ratio.

Adjusting PageRank parameters and comparing results : REPORT

This is my report on Adjusting PageRank parameters and comparing results (v2).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — The effect of adjusting damping factor α and tolerance τ on iterations needed for PageRank computation is studied here. Relative performance of PageRank computation with L1, L2, and L∞ norms used as convergence check, are also compared with six possible mean ratios. It is observed that increasing the damping factor α linearly increases the iterations needed almost exponentially. On the other hand, decreasing the tolerance τ exponentially decreases the iterations needed almost exponentially. On average, PageRank with L∞ norm as convergence check is the fastest, quickly followed by L2 norm, and then L1 norm. For large graphs, above certain tolerance τ values, convergence can occur in a single iteration. On the contrary, below certain tolerance τ values, sensitivity issues can begin to appear, causing computation to halt at maximum iteration limit without convergence. The six mean ratios for relative performance comparison are based on arithmetic, geometric, and harmonic mean, as well as the order of ratio calculation. Among them GM-RATIO, geometric mean followed by ratio calculation, is found to be most stable, followed by AM-RATIO.
Index terms — PageRank algorithm, Parameter adjustment, Convergence function, Sensitivity issues, Relative performance comparison.

Rank adjustment strategies for Dynamic PageRank : REPORT

This is my report on:
Rank adjustment strategies for Dynamic PageRank (v1).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — To avoid calculating ranks of vertices in a dynamic graph from scratch for every snapshot, the ones computed in the previous snapshot of the graph can be used, with adjustment. Four different rank adjustment strategies for dynamic PageRank are studied here. These include zero-fill, 1/N-fill, scaled zero-fill, and scaled 1/N-fill. Results indicate that the scaled 1/N-fill strategy requires the least number of iterations, on average. As long as the graph has no affected dead ends (including dead ends in the previous snapshot), unaffected vertices can be skipped with this adjustment strategy.
Index terms — PageRank algorithm, Dynamic graph, Rank adjustment, Initial ranks.

Effect of stepwise adjustment of Damping factor upon PageRank : REPORT

This is my report on Effect of stepwise adjustment of Damping factor upon PageRank (v1).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — The effect of adjusting damping factor α, from a small initial value α0 to the final desired αf value, upon then iterations needed for PageRank computation is observed. Adjustment of the damping factor is done in one or more steps. Results show no improvement in performance over a fixed damping factor based PageRank.
Index terms — PageRank algorithm, Step-wise adjustment, Damping factor.

What is ARIMA Forecasting and How Can it Be Used for Enterprise Analysis?

What is ARIMA Forecasting and How Can it Be Used for Enterprise Analysis?Smarten Augmented Analytics

The document provides an overview of time series forecasting using ARIMA (Autoregressive Integrated Moving Average) models. It defines the ARIMA model parameters - autoregressive (p), differencing (d), and moving average (q) - and explains how they are used to forecast future values based on past observations. Examples are given to demonstrate identifying the p, d, q values and fitting the ARIMA model to sample time series data. Limitations and use cases for ARIMA forecasting in business are also discussed.Chapter 3 mathematical modeling of dynamic system

The document discusses mathematical modeling of dynamic systems, including obtaining differential equations to represent system dynamics, different representations like transfer functions and impulse response functions, using block diagrams to visualize system components and signal flows, modeling various physical systems like mechanical, electrical, and thermal systems, and representing systems using signal flow graphs. It provides examples of obtaining transfer functions for different system types and using block diagram reduction techniques to find overall transfer functions.

Sensor Fusion Study - Ch13. Nonlinear Kalman Filtering [Ahn Min Sung]

1. The document discusses various nonlinear Kalman filtering techniques, including the extended Kalman filter (EKF), iterated EKF, and second-order EKF.
2. The EKF linearizes the system equations around the current state estimate to apply the Kalman filter equations. Higher-order approaches do additional Taylor series expansions.
3. Parameter estimation with nonlinear filters is also covered, where an augmented state vector is used to jointly estimate the system state and unknown parameters.

Brock Butlett Time Series-Great Lakes

The "Great Lakes" data set is an example of a non-seasonal, non-stationary time series that
experiences a slight upward linear trend. The series is differenced and transformed using
"Box-Cox" in order to stabilize the mean and variance, correcting for stationarity. The best
model fitted for the data was an ARIMA(4,1,0) found by observing the partial and auto
correlation functions. The fit suggested the best estimates for the coefficients via the AIC.
Verified as independent random variables, the residuals of the fitted model were tested for
normality using the McLeod-Li, Ljung-Box, and Shapiro-Wilk test. The model proved to be
an adequate representation of the data providing reasonable predictions for precipitation.

Adjusting PageRank parameters and comparing results : REPORT

This document discusses experiments adjusting PageRank algorithm parameters and comparing results. It is found that increasing the damping factor α increases iterations exponentially, while decreasing the tolerance τ decreases iterations exponentially. PageRank with L∞ norm converges fastest on average, followed by L2 norm then L1 norm. The most stable method for comparing relative performance is the geometric mean ratio.

Adjusting PageRank parameters and comparing results : REPORT

This is my report on Adjusting PageRank parameters and comparing results (v2).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — The effect of adjusting damping factor α and tolerance τ on iterations needed for PageRank computation is studied here. Relative performance of PageRank computation with L1, L2, and L∞ norms used as convergence check, are also compared with six possible mean ratios. It is observed that increasing the damping factor α linearly increases the iterations needed almost exponentially. On the other hand, decreasing the tolerance τ exponentially decreases the iterations needed almost exponentially. On average, PageRank with L∞ norm as convergence check is the fastest, quickly followed by L2 norm, and then L1 norm. For large graphs, above certain tolerance τ values, convergence can occur in a single iteration. On the contrary, below certain tolerance τ values, sensitivity issues can begin to appear, causing computation to halt at maximum iteration limit without convergence. The six mean ratios for relative performance comparison are based on arithmetic, geometric, and harmonic mean, as well as the order of ratio calculation. Among them GM-RATIO, geometric mean followed by ratio calculation, is found to be most stable, followed by AM-RATIO.
Index terms — PageRank algorithm, Parameter adjustment, Convergence function, Sensitivity issues, Relative performance comparison.

Rank adjustment strategies for Dynamic PageRank : REPORT

This is my report on:
Rank adjustment strategies for Dynamic PageRank (v1).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — To avoid calculating ranks of vertices in a dynamic graph from scratch for every snapshot, the ones computed in the previous snapshot of the graph can be used, with adjustment. Four different rank adjustment strategies for dynamic PageRank are studied here. These include zero-fill, 1/N-fill, scaled zero-fill, and scaled 1/N-fill. Results indicate that the scaled 1/N-fill strategy requires the least number of iterations, on average. As long as the graph has no affected dead ends (including dead ends in the previous snapshot), unaffected vertices can be skipped with this adjustment strategy.
Index terms — PageRank algorithm, Dynamic graph, Rank adjustment, Initial ranks.

Effect of stepwise adjustment of Damping factor upon PageRank : REPORT

This is my report on Effect of stepwise adjustment of Damping factor upon PageRank (v1).
While doing research work under Prof. Dip Banerjee, Prof. Kishore Kothapalli.
Abstract — The effect of adjusting damping factor α, from a small initial value α0 to the final desired αf value, upon then iterations needed for PageRank computation is observed. Adjustment of the damping factor is done in one or more steps. Results show no improvement in performance over a fixed damping factor based PageRank.
Index terms — PageRank algorithm, Step-wise adjustment, Damping factor.

What is ARIMA Forecasting and How Can it Be Used for Enterprise Analysis?

What is ARIMA Forecasting and How Can it Be Used for Enterprise Analysis?Smarten Augmented Analytics

The document provides an overview of time series forecasting using ARIMA (Autoregressive Integrated Moving Average) models. It defines the ARIMA model parameters - autoregressive (p), differencing (d), and moving average (q) - and explains how they are used to forecast future values based on past observations. Examples are given to demonstrate identifying the p, d, q values and fitting the ARIMA model to sample time series data. Limitations and use cases for ARIMA forecasting in business are also discussed.Chapter 3 mathematical modeling of dynamic system

The document discusses mathematical modeling of dynamic systems, including obtaining differential equations to represent system dynamics, different representations like transfer functions and impulse response functions, using block diagrams to visualize system components and signal flows, modeling various physical systems like mechanical, electrical, and thermal systems, and representing systems using signal flow graphs. It provides examples of obtaining transfer functions for different system types and using block diagram reduction techniques to find overall transfer functions.

Sensor Fusion Study - Ch13. Nonlinear Kalman Filtering [Ahn Min Sung]

1. The document discusses various nonlinear Kalman filtering techniques, including the extended Kalman filter (EKF), iterated EKF, and second-order EKF.
2. The EKF linearizes the system equations around the current state estimate to apply the Kalman filter equations. Higher-order approaches do additional Taylor series expansions.
3. Parameter estimation with nonlinear filters is also covered, where an augmented state vector is used to jointly estimate the system state and unknown parameters.

Brock Butlett Time Series-Great Lakes

The "Great Lakes" data set is an example of a non-seasonal, non-stationary time series that
experiences a slight upward linear trend. The series is differenced and transformed using
"Box-Cox" in order to stabilize the mean and variance, correcting for stationarity. The best
model fitted for the data was an ARIMA(4,1,0) found by observing the partial and auto
correlation functions. The fit suggested the best estimates for the coefficients via the AIC.
Verified as independent random variables, the residuals of the fitted model were tested for
normality using the McLeod-Li, Ljung-Box, and Shapiro-Wilk test. The model proved to be
an adequate representation of the data providing reasonable predictions for precipitation.

Mathematical Modelling of Control Systems

Different types of mathematical modeling in control systems [which include Mathematical Modeling of Mechanical and Electrical System (which further includes, Force-Voltage and Force-Current Analogies)]

X bar and-r_charts

This procedure generates X-bar and R control charts to monitor the mean and variation of processes. It estimates parameters like the grand mean and standard deviation from subgroup data. It then calculates control limits for X-bar and R charts to detect points that are out of control. It can also perform runs tests to identify unnatural patterns caused by assignable causes.

Isen 614 project presentation

Advanced quality control - Texas A&M university. Manufacturing process control using multivariate control charts

Sensor Fusion Study - Ch7. Kalman Filter Generalizations [김영범]

This document discusses several generalizations and modifications that can be made to the standard Kalman filter. Section 7.3 describes how a steady-state Kalman filter can be used instead of a time-varying filter when system dynamics are time-invariant. Section 7.4 discusses a fading memory filter that discounts older measurements to address cases when system dynamics are imperfectly known. Section 7.5 presents several approaches to incorporate state equality and inequality constraints into the Kalman filter formulation, including model reduction, projection approaches, and probability density function truncation.

Sensor Fusion Study - Ch10. Additional topics in kalman filter [Stella Seoyeo...

This document discusses additional topics related to Kalman filtering, including verifying filter performance, multiple model estimation, reduced-order filtering, robust filtering, and handling delayed measurements. Specific topics covered include using innovations statistics to verify filters, running multiple filters in parallel with different models, reducing filter order to lower computational costs, making filters more robust to model uncertainties, and modifying filters to incorporate out-of-sequence measurements.

Computing Transformations Spring2005

This document discusses various data transformations that can be used to satisfy assumptions of normality, homogeneity of variance, and linearity when analyzing metric variables. It describes how to compute logarithmic, square root, inverse, and square transformations in SPSS. Adjustments may need to be added to the values when computing the transformations depending on whether the original variable is positively or negatively skewed. The transformed variables are added as new variables to the SPSS data file.

Sensor Fusion Study - Ch5. The discrete-time Kalman filter [박정은]

The document summarizes key concepts about the discrete-time Kalman filter. It describes how the Kalman filter uses a set of mathematical equations to estimate the state of a dynamic system based on a series of measurements over time that contain noise. These equations estimate the state mean and covariance to minimize the error between the true state and the estimated state. The derivation of the filter equations is shown, including the time update and measurement update equations. Issues like divergence due to modeling errors and numerical problems are discussed, along with remedies like adding fictitious process noise.

Sensor Fusion Study - Ch8. The Continuous-Time Kalman Filter [이해구]

This chapter discusses the continuous-time Kalman filter. It begins by comparing discrete-time and continuous-time systems, then derives the continuous-time Kalman filter equations. It also describes alternative methods for solving the Riccati equation such as transition matrix approach and square root filtering. Finally, it generalizes the continuous-time Kalman filter to cases with correlated process and measurement noise, as well as colored noise.

Logarithmic transformations

1. The document discusses logarithmic transformations, which can be used to transform non-linear data into a linear format to better model exponential relationships.
2. There are two options for logarithmic transformations: taking the log of just the response variable y, or taking the log of both the explanatory variable x and the response variable y.
3. Graphing the transformed data allows one to determine which option produces a more linear relationship and thus the better transformation to use.

Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...

This Time Series Analysis (Part-2) in R presentation will help you understand what is ARIMA model, what is correlation & auto-correlation and you will alose see a use case implementation in which we forecast sales of air-tickets using ARIMA and at the end, we will also how to validate a model using Ljung-Box text. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this " Time Series in R presentation " -
1. Introduction to ARIMA model
2. Auto-correlation & partial auto-correlation
3. Use case - Forecast the sales of air-tickets using ARIMA
4. Model validating using Ljung-Box test
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
Why learn Data Science with R?
1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/

Time Series - Auto Regressive Models

Time Series basic concepts and ARIMA family of models. There is an associated video session along with code in github: https://github.com/bhaskatripathi/timeseries-autoregressive-models
https://drive.google.com/file/d/1yXffXQlL6i4ufQLSpFFrJgymhHNXL1Mf/view?usp=sharing

SPSSAssignment2_Report_BerkeleyCTeate

- The Pennsylvania Department of Highways analyzed the effect of specialized crews and a quality improvement initiative on the cost of manual pothole patching.
- Data from 67 county maintenance units was examined for variables like crew specialization, patching quality, production rates, and environmental factors.
- Preliminary analysis found lower average costs associated with higher levels of crew specialization and patching quality. Scatterplots also indicated moderate correlations between lower costs and increased specialization or quality.
- The correlation matrix identified several variables, like specialization, quality, road miles, and weather, that significantly correlated with patching costs.

Isen 614 project report

Advanced quality control - Texas A&M university. Manufacturing process control using multivariate control charts

AR model

This document discusses methods for selecting the order of an autoregressive (AR) model. It explains that AR models depend only on previous outputs and have poles but no zeros. Several criteria for selecting the optimal AR model order are presented, including the Akaike Information Criterion (AIC) and Finite Prediction Error (FPE) criterion. Higher order models fit the data better but can introduce spurious peaks, so the goal is to minimize criteria like AIC or FPE to find the best balance. The document concludes that while these criteria provide guidance, the optimal order depends on the specific data, and inconsistencies can exist between the different methods.

Aristotle boyd martin-peci_poster_2017

Poster based on research on investigating the non-linear response of a synchronous machine to variations in system parameters (torque and damping), demonstrating the existence of a bifurcation curve within the parameter space. Response was visualized using state space diagrams. This poster was presented at the Power and Energy Conference at the University of Illinois (PECI) in Spring 2017.

R chart

Control charts consist of three horizontal lines: a central line showing the process average, an upper control limit, and a lower control limit. Variables are quality characteristics that can be measured and expressed quantitatively. An R chart plots sample ranges to control variability within subgroups. To set up an R chart, sample ranges are plotted against sample number, with upper, central, and lower control limits calculated using constants D3 and D4 that depend on sample size.

Systemic Arterial Pulse Pressure Analysis

This document describes using a mathematical function to model systemic arterial pulse pressure over time. It provides examples of:
1) Calculating systolic, diastolic, and pulse pressures using given parameters in the function.
2) Plotting arterial pressure over one period.
3) Increasing stroke volume and observing higher systolic, diastolic, and pulse pressures.
4) Decreasing resistance through exercise and the effect on pressures.
5) Deriving that average pressure is directly proportional to stroke volume and resistance.
6) Plotting pulse pressure over time with random fluctuations in stroke volume and period. Longer periods resulted in higher pulse pressure.

Av 738- Adaptive Filtering - Wiener Filters[wk 3]

The document discusses the derivation and properties of Wiener filters, which are linear filters that minimize the mean square error between the desired signal and the estimate. Specifically:
- It derives the Weiner-Hopf equation, which provides the condition for optimal filter weights to minimize the mean square error.
- It shows that the optimal filter output and minimum error are orthogonal.
- It discusses how the Weiner filter can be used for applications like noise cancellation by estimating the desired signal using two microphones.
- It provides an example of applying a Weiner filter to cancel noise from a signal measured by two microphones mounted on a pilot's helmet.

Sensor Fusion Study - Ch3. Least Square Estimation [강소라, Stella, Hayden]

This document discusses Wiener filtering and recursive least squares estimation. It begins with an introduction to Wiener filtering, providing an overview of its history and development. It then discusses how the power spectrum of a stochastic process changes when passed through a linear time-invariant system. Next, it formulates the problem of using a linear filter to extract a signal from additive noise. It derives expressions for the power spectrum of the error and its variance. Finally, it considers optimizing a parametric filter by assuming the optimal filter is a first-order low-pass filter and that the signal and noise spectra are known forms. It derives an expression for the optimal parameter T based on minimizing the error variance.

Detection & Estimation Theory

This document introduces several concepts in estimation theory, including Bayesian parameter estimation, non-Bayesian parameter estimation, maximum likelihood estimation, and the Cramér-Rao lower bound. It provides examples of estimating parameters for linear and nonlinear models from observed data using different cost functions and derivation of the mean square error, maximum a posteriori, and maximum likelihood estimates.

Linear regression [Theory and Application (In physics point of view) using py...

Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.

R analysis of covariance

This presentation educates you about R - Logistic Regression, ANCOVA Analysis and Comparing Two Models with basic syntax.
For more topics stay tuned with Learnbay.

Mathematical Modelling of Control Systems

Different types of mathematical modeling in control systems [which include Mathematical Modeling of Mechanical and Electrical System (which further includes, Force-Voltage and Force-Current Analogies)]

X bar and-r_charts

This procedure generates X-bar and R control charts to monitor the mean and variation of processes. It estimates parameters like the grand mean and standard deviation from subgroup data. It then calculates control limits for X-bar and R charts to detect points that are out of control. It can also perform runs tests to identify unnatural patterns caused by assignable causes.

Isen 614 project presentation

Advanced quality control - Texas A&M university. Manufacturing process control using multivariate control charts

Sensor Fusion Study - Ch7. Kalman Filter Generalizations [김영범]

This document discusses several generalizations and modifications that can be made to the standard Kalman filter. Section 7.3 describes how a steady-state Kalman filter can be used instead of a time-varying filter when system dynamics are time-invariant. Section 7.4 discusses a fading memory filter that discounts older measurements to address cases when system dynamics are imperfectly known. Section 7.5 presents several approaches to incorporate state equality and inequality constraints into the Kalman filter formulation, including model reduction, projection approaches, and probability density function truncation.

Sensor Fusion Study - Ch10. Additional topics in kalman filter [Stella Seoyeo...

This document discusses additional topics related to Kalman filtering, including verifying filter performance, multiple model estimation, reduced-order filtering, robust filtering, and handling delayed measurements. Specific topics covered include using innovations statistics to verify filters, running multiple filters in parallel with different models, reducing filter order to lower computational costs, making filters more robust to model uncertainties, and modifying filters to incorporate out-of-sequence measurements.

Computing Transformations Spring2005

This document discusses various data transformations that can be used to satisfy assumptions of normality, homogeneity of variance, and linearity when analyzing metric variables. It describes how to compute logarithmic, square root, inverse, and square transformations in SPSS. Adjustments may need to be added to the values when computing the transformations depending on whether the original variable is positively or negatively skewed. The transformed variables are added as new variables to the SPSS data file.

Sensor Fusion Study - Ch5. The discrete-time Kalman filter [박정은]

The document summarizes key concepts about the discrete-time Kalman filter. It describes how the Kalman filter uses a set of mathematical equations to estimate the state of a dynamic system based on a series of measurements over time that contain noise. These equations estimate the state mean and covariance to minimize the error between the true state and the estimated state. The derivation of the filter equations is shown, including the time update and measurement update equations. Issues like divergence due to modeling errors and numerical problems are discussed, along with remedies like adding fictitious process noise.

Sensor Fusion Study - Ch8. The Continuous-Time Kalman Filter [이해구]

This chapter discusses the continuous-time Kalman filter. It begins by comparing discrete-time and continuous-time systems, then derives the continuous-time Kalman filter equations. It also describes alternative methods for solving the Riccati equation such as transition matrix approach and square root filtering. Finally, it generalizes the continuous-time Kalman filter to cases with correlated process and measurement noise, as well as colored noise.

Logarithmic transformations

1. The document discusses logarithmic transformations, which can be used to transform non-linear data into a linear format to better model exponential relationships.
2. There are two options for logarithmic transformations: taking the log of just the response variable y, or taking the log of both the explanatory variable x and the response variable y.
3. Graphing the transformed data allows one to determine which option produces a more linear relationship and thus the better transformation to use.

Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...

This Time Series Analysis (Part-2) in R presentation will help you understand what is ARIMA model, what is correlation & auto-correlation and you will alose see a use case implementation in which we forecast sales of air-tickets using ARIMA and at the end, we will also how to validate a model using Ljung-Box text. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this " Time Series in R presentation " -
1. Introduction to ARIMA model
2. Auto-correlation & partial auto-correlation
3. Use case - Forecast the sales of air-tickets using ARIMA
4. Model validating using Ljung-Box test
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
Why learn Data Science with R?
1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/

Time Series - Auto Regressive Models

Time Series basic concepts and ARIMA family of models. There is an associated video session along with code in github: https://github.com/bhaskatripathi/timeseries-autoregressive-models
https://drive.google.com/file/d/1yXffXQlL6i4ufQLSpFFrJgymhHNXL1Mf/view?usp=sharing

SPSSAssignment2_Report_BerkeleyCTeate

- The Pennsylvania Department of Highways analyzed the effect of specialized crews and a quality improvement initiative on the cost of manual pothole patching.
- Data from 67 county maintenance units was examined for variables like crew specialization, patching quality, production rates, and environmental factors.
- Preliminary analysis found lower average costs associated with higher levels of crew specialization and patching quality. Scatterplots also indicated moderate correlations between lower costs and increased specialization or quality.
- The correlation matrix identified several variables, like specialization, quality, road miles, and weather, that significantly correlated with patching costs.

Isen 614 project reportAdvanced quality control - Texas A&M university. Manufacturing process control using multivariate control charts

AR model

This document discusses methods for selecting the order of an autoregressive (AR) model. It explains that AR models depend only on previous outputs and have poles but no zeros. Several criteria for selecting the optimal AR model order are presented, including the Akaike Information Criterion (AIC) and Finite Prediction Error (FPE) criterion. Higher order models fit the data better but can introduce spurious peaks, so the goal is to minimize criteria like AIC or FPE to find the best balance. The document concludes that while these criteria provide guidance, the optimal order depends on the specific data, and inconsistencies can exist between the different methods.

Aristotle boyd martin-peci_poster_2017

Poster based on research on investigating the non-linear response of a synchronous machine to variations in system parameters (torque and damping), demonstrating the existence of a bifurcation curve within the parameter space. Response was visualized using state space diagrams. This poster was presented at the Power and Energy Conference at the University of Illinois (PECI) in Spring 2017.

R chart

Control charts consist of three horizontal lines: a central line showing the process average, an upper control limit, and a lower control limit. Variables are quality characteristics that can be measured and expressed quantitatively. An R chart plots sample ranges to control variability within subgroups. To set up an R chart, sample ranges are plotted against sample number, with upper, central, and lower control limits calculated using constants D3 and D4 that depend on sample size.

Systemic Arterial Pulse Pressure Analysis

This document describes using a mathematical function to model systemic arterial pulse pressure over time. It provides examples of:
1) Calculating systolic, diastolic, and pulse pressures using given parameters in the function.
2) Plotting arterial pressure over one period.
3) Increasing stroke volume and observing higher systolic, diastolic, and pulse pressures.
4) Decreasing resistance through exercise and the effect on pressures.
5) Deriving that average pressure is directly proportional to stroke volume and resistance.
6) Plotting pulse pressure over time with random fluctuations in stroke volume and period. Longer periods resulted in higher pulse pressure.

Av 738- Adaptive Filtering - Wiener Filters[wk 3]

The document discusses the derivation and properties of Wiener filters, which are linear filters that minimize the mean square error between the desired signal and the estimate. Specifically:
- It derives the Weiner-Hopf equation, which provides the condition for optimal filter weights to minimize the mean square error.
- It shows that the optimal filter output and minimum error are orthogonal.
- It discusses how the Weiner filter can be used for applications like noise cancellation by estimating the desired signal using two microphones.
- It provides an example of applying a Weiner filter to cancel noise from a signal measured by two microphones mounted on a pilot's helmet.

Sensor Fusion Study - Ch3. Least Square Estimation [강소라, Stella, Hayden]

This document discusses Wiener filtering and recursive least squares estimation. It begins with an introduction to Wiener filtering, providing an overview of its history and development. It then discusses how the power spectrum of a stochastic process changes when passed through a linear time-invariant system. Next, it formulates the problem of using a linear filter to extract a signal from additive noise. It derives expressions for the power spectrum of the error and its variance. Finally, it considers optimizing a parametric filter by assuming the optimal filter is a first-order low-pass filter and that the signal and noise spectra are known forms. It derives an expression for the optimal parameter T based on minimizing the error variance.

Detection & Estimation Theory

This document introduces several concepts in estimation theory, including Bayesian parameter estimation, non-Bayesian parameter estimation, maximum likelihood estimation, and the Cramér-Rao lower bound. It provides examples of estimating parameters for linear and nonlinear models from observed data using different cost functions and derivation of the mean square error, maximum a posteriori, and maximum likelihood estimates.

Mathematical Modelling of Control Systems

Mathematical Modelling of Control Systems

X bar and-r_charts

X bar and-r_charts

Isen 614 project presentation

Isen 614 project presentation

Sensor Fusion Study - Ch7. Kalman Filter Generalizations [김영범]

Sensor Fusion Study - Ch7. Kalman Filter Generalizations [김영범]

Sensor Fusion Study - Ch10. Additional topics in kalman filter [Stella Seoyeo...

Sensor Fusion Study - Ch10. Additional topics in kalman filter [Stella Seoyeo...

Computing Transformations Spring2005

Computing Transformations Spring2005

Sensor Fusion Study - Ch5. The discrete-time Kalman filter [박정은]

Sensor Fusion Study - Ch5. The discrete-time Kalman filter [박정은]

Sensor Fusion Study - Ch8. The Continuous-Time Kalman Filter [이해구]

Sensor Fusion Study - Ch8. The Continuous-Time Kalman Filter [이해구]

Logarithmic transformations

Logarithmic transformations

Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...

Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...

Time Series - Auto Regressive Models

Time Series - Auto Regressive Models

SPSSAssignment2_Report_BerkeleyCTeate

SPSSAssignment2_Report_BerkeleyCTeate

Isen 614 project report

Isen 614 project report

AR model

AR model

Aristotle boyd martin-peci_poster_2017

Aristotle boyd martin-peci_poster_2017

R chart

R chart

Systemic Arterial Pulse Pressure Analysis

Systemic Arterial Pulse Pressure Analysis

Av 738- Adaptive Filtering - Wiener Filters[wk 3]

Av 738- Adaptive Filtering - Wiener Filters[wk 3]

Sensor Fusion Study - Ch3. Least Square Estimation [강소라, Stella, Hayden]

Sensor Fusion Study - Ch3. Least Square Estimation [강소라, Stella, Hayden]

Detection & Estimation Theory

Detection & Estimation Theory

Linear regression [Theory and Application (In physics point of view) using py...

Machine-learning models are behind many recent technological advances, including high-accuracy translations of the text and self-driving cars. They are also increasingly used by researchers to help in solving physics problems, like Finding new phases of matter, Detecting interesting outliers
in data from high-energy physics experiments, Founding astronomical objects are known as gravitational lenses in maps of the night sky etc. The rudimentary algorithm that every Machine Learning enthusiast starts with is a linear regression algorithm. In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent
variables). Linear regression analysis (least squares) is used in a physics lab to prepare the computer-aided report and to fit data. In this article, the application is made to experiment: 'DETERMINATION OF DIELECTRIC CONSTANT OF NON-CONDUCTING LIQUIDS'. The entire computation is made through Python 3.6 programming language in this article.

R analysis of covariance

This presentation educates you about R - Logistic Regression, ANCOVA Analysis and Comparing Two Models with basic syntax.
For more topics stay tuned with Learnbay.

tw1979 Exercise 1 Report

This document summarizes an exercise involving calculating the inverse of square matrices in three ways: analytically, using LU decomposition, and singular value decomposition. It finds that analytical calculation becomes impractically slow for matrices larger than order 13, while LU decomposition and SVD using GNU Scientific Library functions can calculate the inverse of matrices up to order 350 in under 20 seconds. SVD is found to be slightly more efficient than LU decomposition for higher order matrices. Accuracy is also compared when the input matrix is close to singular, finding SVD returns the most accurate inverse.

working with python

Linear regression and logistic regression are two machine learning algorithms that can be implemented in Python. Linear regression is used for predictive analysis to find relationships between variables, while logistic regression is used for classification with binary dependent variables. Support vector machines (SVMs) are another algorithm that finds the optimal hyperplane to separate data points and maximize the margin between the classes. Key terms discussed include cost functions, gradient descent, confusion matrices, and ROC curves. Code examples are provided to demonstrate implementing linear regression, logistic regression, and SVM in Python using scikit-learn.

Integral method to analyze reaction kinetics

1) There are two methods for analyzing kinetic data - the integral method and the differential method.
2) The integral method involves guessing a rate equation and integrating to predict a linear concentration-time relationship. The differential method analyzes rate directly from concentration-time data without integration.
3) An example reaction is analyzed using both methods. The integral method indicates first-order kinetics while the differential method derives a rate constant.

Building the Professional of 2020: An Approach to Business Change Process Int...

Building the Professional of 2020: An Approach to Business Change Process Int...Dr Harris Apostolopoulos EMBA, PfMP, PgMP, PMP, IPMO-E

CRAM (Change Risk Assessment Model) is a novel model approach which can significantly contribute to the missing formality of business models especially in the change(s) risk assessment area.
Project Management has long established the need for risk management techniques to be utilised in the succinct definition of associated risks in projects and agreement on countervailing actions as an aim to reduce scope creep, increase the probability of on-time and in-budget delivery.
Uncontrolled changes, regardless of size and complexity, can certainly pose as risks, of any magnitude, to projects and affect project success or even an organisation’s coherence.
Chapter Two PPT Lecture - Part One.ppt

The document discusses organizing and summarizing data using frequency tables, histograms, and ogives. It provides examples of creating a frequency table and histogram to organize one-way commuting distance data from 60 workers. It also demonstrates how to make a cumulative frequency table and ogive to summarize daily high temperature data from a ski season. Key terms like class width, class boundaries, and distribution shapes are explained.

Applied Numerical Methods Curve Fitting: Least Squares Regression, Interpolation

Correction with the misspelled langrange.
and credits to the owners of the pictures (Fantasmagoria01, eugene-kukulka, vooga, and etc.) . I do not own all of the pictures used as background sorry to those who aren't tagged.
The presentation contains topics from Applied Numerical Methods with MATHLAB for Engineers and Scientist 6th and International Edition.

RS

Alexander Litvinenko's research interests include developing efficient numerical methods for solving stochastic PDEs using low-rank tensor approximations. He has made contributions in areas such as fast techniques for solving stochastic PDEs using tensor approximations, inexpensive functional approximations of Bayesian updating formulas, and modeling uncertainties in parameters, coefficients, and computational geometry using probabilistic methods. His current research focuses on uncertainty quantification, Bayesian updating techniques, and developing scalable and parallel methods using hierarchical matrices.

Simple lin regress_inference

This document provides an overview of simple linear regression analysis. It discusses estimating regression coefficients using the least squares method, interpreting the regression equation, assessing model fit using measures like the standard error of the estimate and coefficient of determination, testing hypotheses about regression coefficients, and using the regression model to make predictions.

Ann a Algorithms notes

Gradient descent is an optimization algorithm used to minimize a cost function by iteratively adjusting parameter values in the direction of the steepest descent. It works by calculating the derivative of the cost function to determine which direction leads to lower cost, then taking a step in that direction. This process repeats until reaching a minimum. Gradient descent is simple but requires knowing the gradient of the cost function. Backpropagation extends gradient descent to neural networks by propagating error backwards from the output to calculate gradients to update weights.

Comparing the methods of Estimation of Three-Parameter Weibull distribution

This document compares different methods for estimating the parameters of a three-parameter Weibull distribution from sample data, including graphical methods, trial and error, Jiang/Murthy's approach, and maximum likelihood estimation. It applies these methods to simulated sample data from a Weibull distribution with known parameters to estimate the location, scale, and shape parameters. The trial and error method uses residual sum of squares to select the location parameter that provides the best fit. The maximum likelihood method derives equations that are solved numerically. The results show that all methods can estimate the parameters reasonably well, though accuracy varies depending on the full or censored sample size.

Using the Componentwise Metropolis-Hastings Algorithm to Sample from the Join...

Markov Chain Monte Carlo (MCMC) methods provide a way to sample from a distribution (e.g., the joint posterior distribution for the parameters of a Bayesian model). These methods are useful when analytic solutions for parameter estimations do not exist. If the Markov chain is long, the sampled random variables are (approximately) identically distributed, but they are not independent because in a Markov chain each random variable depends on the previous one. However, because the Ergodic Theorem applies to MCMC methods, the chains converge (with probability one) to the stationary distribution, which for our purposes is the Bayesian joint posterior distribution.
MCMC methods are frequently implemented using a Gibbs sampler. This, however, requires knowledge of the parameters' conditional distributions, which are frequently not available. In this case, another MCMC method, called the Metropolis-Hastings algorithm, can be used. The Metropolis-Hastings algorithm is a type of acceptance/rejection method. It requires a candidate-generating distribution, also called proposal distribution. Ideally, the proposal distribution should be similar to the posterior distribution, but any distribution with the same support as the posterior is possible.
The Metropolis-Hastings algorithm generalizes to multidimensional distributions. In the multidimensional case, there are two types of algorithms ― the "regular" algorithm and the "componentwise" algorithm. Whereas the "regular" algorithm computes a full proposal vector at each step, the "componentwise" algorithm, which is implemented here for a binomial regression model, updates each component at a time, so that the proposals for all the components are evaluated, i.e., accepted or rejected, in turn.

Data Analysis Homework Help

I am Stacy L. I am a Matlab Assignment Expert at matlabassignmentexperts.com. I hold a Master's in Matlab, University of Houston. I have been helping students with their homework for the past 9 years. I solve assignments related to Data Analysis.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Data Analysis Assignments.

Chapter 18,19

This document discusses techniques for evaluating and improving statistical models, including regularized regression methods. It covers residuals, Q-Q plots, histograms to evaluate model fit. It also discusses comparing models using ANOVA, AIC, BIC, cross-validation, bootstrapping. Regularization methods like lasso, ridge and elastic net are introduced. Parallel computing is used to more efficiently select hyperparameters for elastic net models.

Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...

Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.

2014-mo444-practical-assignment-04-paulo_faria

The document discusses applying machine learning techniques to identify compiler optimizations that impact program performance. It used classification trees to analyze a dataset containing runtime measurements for 19 programs compiled with different combinations of 45 LLVM optimizations. The trees identified optimizations like SROA and inlining that generally improved performance across programs. Analysis of individual programs found some variations, but also common optimizations like SROA and simplifying the control flow graph. Precision, accuracy, and AUC metrics were used to evaluate the trees' ability to classify optimizations for best runtime.

Adjusting OpenMP PageRank : SHORT REPORT / NOTES

For massive graphs that fit in RAM, but not in GPU memory, it is possible to take
advantage of a shared memory system with multiple CPUs, each with multiple cores, to
accelerate pagerank computation. If the NUMA architecture of the system is properly taken
into account with good vertex partitioning, the speedup can be significant. To take steps in
this direction, experiments are conducted to implement pagerank in OpenMP using two
different approaches, uniform and hybrid. The uniform approach runs all primitives required
for pagerank in OpenMP mode (with multiple threads). On the other hand, the hybrid
approach runs certain primitives in sequential mode (i.e., sumAt, multiply).

Regression with Time Series Data

Any business and economic applications of forecasting involve time series data. Re-gression models can be fit to monthly, quarterly, or yearly data using the techniques de-scribed in previous chapters. However, because data collected over time tend to exhibit trends, seasonal patterns, and so forth, observations in different time periods are re¬lated or autocorrelated. That is, for time series data, the sample of observations cannot be regarded as a random sample. Problems of interpretation can arise when standard regression methods are applied to observations that are related to one another over time. Fitting regression models to time series data must be done with considerable care.

Algorithmic optimizations for Dynamic Monolithic PageRank (from STICD) : SHOR...

Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.

Linear regression [Theory and Application (In physics point of view) using py...

Linear regression [Theory and Application (In physics point of view) using py...

R analysis of covariance

R analysis of covariance

tw1979 Exercise 1 Report

tw1979 Exercise 1 Report

working with python

working with python

Integral method to analyze reaction kinetics

Integral method to analyze reaction kinetics

Building the Professional of 2020: An Approach to Business Change Process Int...

Building the Professional of 2020: An Approach to Business Change Process Int...

Chapter Two PPT Lecture - Part One.ppt

Chapter Two PPT Lecture - Part One.ppt

Applied Numerical Methods Curve Fitting: Least Squares Regression, Interpolation

Applied Numerical Methods Curve Fitting: Least Squares Regression, Interpolation

RS

RS

Simple lin regress_inference

Simple lin regress_inference

Ann a Algorithms notes

Ann a Algorithms notes

Comparing the methods of Estimation of Three-Parameter Weibull distribution

Comparing the methods of Estimation of Three-Parameter Weibull distribution

Using the Componentwise Metropolis-Hastings Algorithm to Sample from the Join...

Using the Componentwise Metropolis-Hastings Algorithm to Sample from the Join...

Data Analysis Homework Help

Data Analysis Homework Help

Chapter 18,19

Chapter 18,19

Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...

Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...

2014-mo444-practical-assignment-04-paulo_faria

2014-mo444-practical-assignment-04-paulo_faria

Adjusting OpenMP PageRank : SHORT REPORT / NOTES

Adjusting OpenMP PageRank : SHORT REPORT / NOTES

Regression with Time Series Data

Regression with Time Series Data

Algorithmic optimizations for Dynamic Monolithic PageRank (from STICD) : SHOR...

Algorithmic optimizations for Dynamic Monolithic PageRank (from STICD) : SHOR...

About TrueTime, Spanner, Clock synchronization, CAP theorem, Two-phase lockin...

TrueTime is a service that enables the use of globally synchronized clocks, with bounded error. It returns a time interval that is guaranteed to contain the clock’s actual time for some time during the call’s execution. If two intervals do not overlap, then we know calls were definitely ordered in real time. In general, synchronized clocks can be used to avoid communication in a distributed system.
The underlying source of time is a combination of GPS receivers and atomic clocks. As there are “time masters” in every datacenter (redundantly), it is likely that both sides of a partition would continue to enjoy accurate time. Individual nodes however need network connectivity to the masters, and without it their clocks will drift. Thus, during a partition their intervals slowly grow wider over time, based on bounds on the rate of local clock drift. Operations depending on TrueTime, such as Paxos leader election or transaction commits, thus have to wait a little longer, but the operation still completes (assuming the 2PC and quorum communication are working).

Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...

Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.

Adjusting Bitset for graph : SHORT REPORT / NOTES

Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is commonly used for efficient graph computations. Unfortunately, using CSR for dynamic graphs is impractical since addition/deletion of a single edge can require on average (N+M)/2 memory accesses, in order to update source-offsets and destination-indices. A common approach is therefore to store edge-lists/destination-indices as an array of arrays, where each edge-list is an array belonging to a vertex. While this is good enough for small graphs, it quickly becomes a bottleneck for large graphs. What causes this bottleneck depends on whether the edge-lists are sorted or unsorted. If they are sorted, checking for an edge requires about log(E) memory accesses, but adding an edge on average requires E/2 accesses, where E is the number of edges of a given vertex. Note that both addition and deletion of edges in a dynamic graph require checking for an existing edge, before adding or deleting it. If edge lists are unsorted, checking for an edge requires around E/2 memory accesses, but adding an edge requires only 1 memory access.

Adjusting primitives for graph : SHORT REPORT / NOTES

Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).

Experiments with Primitive operations : SHORT REPORT / NOTES

This includes:
- Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
- Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
- Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
- Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).

PageRank Experiments : SHORT REPORT / NOTES

This includes:
- Adjusting data types for rank vector
- Adjusting Pagerank parameters
- Adjusting Sequential approach
- Adjusting OpenMP approach
- Comparing sequential approach
- Adjusting Monolithic (Sequential) optimizations (from STICD)
- Adjusting Levelwise (STICD) approach
- Comparing Levelwise (STICD) approach
- Adjusting ranks for dynamic graphs
- Adjusting Levelwise (STICD) dynamic approach
- Comparing dynamic approach with static
- Adjusting Monolithic CUDA approach
- Adjusting Monolithic CUDA optimizations (from STICD)
- Adjusting Levelwise (STICD) CUDA approach
- Comparing Levelwise (STICD) CUDA approach
- Comparing dynamic CUDA approach with static
- Comparing dynamic optimized CUDA approach with static

word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings o...

Below are the important points I note from the 2020 paper by Martin Grohe:
- 1-WL distinguishes almost all graphs, in a probabilistic sense
- Classical WL is two dimensional Weisfeiler-Leman
- DeepWL is an unlimited version of WL graph that runs in polynomial time.
- Knowledge graphs are essentially graphs with vertex/edge attributes
ABSTRACT:
Vector representations of graphs and relational structures, whether handcrafted feature vectors or learned representations, enable us to apply standard data analysis and machine learning techniques to the structures. A wide range of methods for generating such embeddings have been studied in the machine learning and knowledge representation literature. However, vector embeddings have received relatively little attention from a theoretical point of view.
Starting with a survey of embedding techniques that have been used in practice, in this paper we propose two theoretical approaches that we see as central for understanding the foundations of vector embeddings. We draw connections between the various approaches and suggest directions for future research.

DyGraph: A Dynamic Graph Generator and Benchmark Suite : NOTES

https://gist.github.com/wolfram77/54c4a14d9ea547183c6c7b3518bf9cd1
There exist a number of dynamic graph generators. Barbasi-Albert model iteratively attach new vertices to pre-exsiting vertices in the graph using preferential attachment (edges to high degree vertices are more likely - rich get richer - Pareto principle). However, graph size increases monotonically, and density of graph keeps increasing (sparsity decreasing).
Gorke's model uses a defined clustering to uniformly add vertices and edges. Purohit's model uses motifs (eg. triangles) to mimick properties of existing dynamic graphs, such as growth rate, structure, and degree distribution. Kronecker graph generators are used to increase size of a given graph, with power-law distribution.
To generate dynamic graphs, we must choose a metric to compare two graphs. Common metrics include diameter, clustering coefficient (modularity?), triangle counting (triangle density?), and degree distribution.
In this paper, the authors propose Dygraph, a dynamic graph generator that uses degree distribution as the only metric. The authors observe that many real-world graphs differ from the power-law distribution at the tail end. To address this issue, they propose binning, where the vertices beyond a certain degree (minDeg = min(deg) s.t. |V(deg)| < H, where H~10 is the number of vertices with a given degree below which are binned) are grouped into bins of degree-width binWidth, max-degree localMax, and number of degrees in bin with at least one vertex binSize (to keep track of sparsity). This helps the authors to generate graphs with a more realistic degree distribution.
The process of generating a dynamic graph is as follows. First the difference between the desired and the current degree distribution is calculated. The authors then create an edge-addition set where each vertex is present as many times as the number of additional incident edges it must recieve. Edges are then created by connecting two vertices randomly from this set, and removing both from the set once connected. Currently, authors reject self-loops and duplicate edges. Removal of edges is done in a similar fashion.
Authors observe that adding edges with power-law properties dominates the execution time, and consider parallelizing DyGraph as part of future work.

Shared memory Parallelism (NOTES)

My notes on shared memory parallelism.
Shared memory is memory that may be simultaneously accessed by multiple programs with an intent to provide communication among them or avoid redundant copies. Shared memory is an efficient means of passing data between programs. Using memory for communication inside a single program, e.g. among its multiple threads, is also referred to as shared memory [REF].

A Dynamic Algorithm for Local Community Detection in Graphs : NOTES

**Community detection methods** can be *global* or *local*. **Global community detection methods** divide the entire graph into groups. Existing global algorithms include:
- Random walk methods
- Spectral partitioning
- Label propagation
- Greedy agglomerative and divisive algorithms
- Clique percolation
https://gist.github.com/wolfram77/b4316609265b5b9f88027bbc491f80b6
There is a growing body of work in *detecting overlapping communities*. **Seed set expansion** is a **local community detection method** where a relevant *seed vertices* of interest are picked and *expanded to form communities* surrounding them. The quality of each community is measured using a *fitness function*.
**Modularity** is a *fitness function* which compares the number of intra-community edges to the expected number in a random-null model. **Conductance** is another popular fitness score that measures the community cut or inter-community edges. Many *overlapping community detection* methods **use a modified ratio** of intra-community edges to all edges with atleast one endpoint in the community.
Andersen et al. use a **Spectral PageRank-Nibble method** which minimizes conductance and is formed by adding vertices in order of decreasing PageRank values. Andersen and Lang develop a **random walk approach** in which some vertices in the seed set may not be placed in the final community. Clauset gives a **greedy method** that *starts from a single vertex* and then iteratively adds neighboring vertices *maximizing the local modularity score*. Riedy et al. **expand multiple vertices** via maximizing modularity.
Several algorithms for **detecting global, overlapping communities** use a *greedy*, *agglomerative approach* and run *multiple separate seed set expansions*. Lancichinetti et al. run **greedy seed set expansions**, each with a *single seed vertex*. Overlapping communities are produced by a sequentially running expansions from a node not yet in a community. Lee et al. use **maximal cliques as seed sets**. Havemann et al. **greedily expand cliques**.
The authors of this paper discuss a dynamic approach for **community detection using seed set expansion**. Simply marking the neighbours of changed vertices is a **naive approach**, and has *severe shortcomings*. This is because *communities can split apart*. The simple updating method *may fail even when it outputs a valid community* in the graph.

Scalable Static and Dynamic Community Detection Using Grappolo : NOTES

A **community** (in a network) is a subset of nodes which are _strongly connected among themselves_, but _weakly connected to others_. Neither the number of output communities nor their size distribution is known a priori. Community detection methods can be divisive or agglomerative. **Divisive methods** use _betweeness centrality_ to **identify and remove bridges** between communities. **Agglomerative methods** greedily **merge two communities** that provide maximum gain in _modularity_. Newman and Girvan have introduced the **modularity metric**. The problem of community detection is then reduced to the problem of modularity maximization which is **NP-complete**. **Louvain method** is a variant of the _agglomerative strategy_, in that is a _multi-level heuristic_.
https://gist.github.com/wolfram77/917a1a4a429e89a0f2a1911cea56314d
In this paper, the authors discuss **four heuristics** for Community detection using the _Louvain algorithm_ implemented upon recently developed **Grappolo**, which is a parallel variant of the Louvain algorithm. They are:
- Vertex following and Minimum label
- Data caching
- Graph coloring
- Threshold scaling
With the **Vertex following** heuristic, the _input is preprocessed_ and all single-degree vertices are merged with their corresponding neighbours. This helps reduce the number of vertices considered in each iteration, and also help initial seeds of communities to be formed. With the **Minimum label heuristic**, when a vertex is making the decision to move to a community and multiple communities provided the same modularity gain, the community with the smallest id is chosen. This helps _minimize or prevent community swaps_. With the **Data caching** heuristic, community information is stored in a vector instead of a map, and is reused in each iteration, but with some additional cost. With the **Vertex ordering via Graph coloring** heuristic, _distance-k coloring_ of graphs is performed in order to group vertices into colors. Then, each set of vertices (by color) is processed _concurrently_, and synchronization is performed after that. This enables us to mimic the behaviour of the serial algorithm. Finally, with the **Threshold scaling** heuristic, _successively smaller values of modularity threshold_ are used as the algorithm progresses. This allows the algorithm to converge faster, and it has been observed a good modularity score as well.
From the results, it appears that _graph coloring_ and _threshold scaling_ heuristics do not always provide a speedup and this depends upon the nature of the graph. It would be interesting to compare the heuristics against baseline approaches. Future work can include _distributed memory implementations_, and _community detection on streaming graphs_.

Application Areas of Community Detection: A Review : NOTES

This is a short review of Community detection methods (on graphs), and their applications. A **community** is a subset of a network whose members are *highly connected*, but *loosely connected* to others outside their community. Different community detection methods *can return differing communities* these algorithms are **heuristic-based**. **Dynamic community detection** involves tracking the *evolution of community structure* over time.
https://gist.github.com/wolfram77/09e64d6ba3ef080db5558feb2d32fdc0
Communities can be of the following **types**:
- Disjoint
- Overlapping
- Hierarchical
- Local.
The following **static** community detection **methods** exist:
- Spectral-based
- Statistical inference
- Optimization
- Dynamics-based
The following **dynamic** community detection **methods** exist:
- Independent community detection and matching
- Dependent community detection (evolutionary)
- Simultaneous community detection on all snapshots
- Dynamic community detection on temporal networks
**Applications** of community detection include:
- Criminal identification
- Fraud detection
- Criminal activities detection
- Bot detection
- Dynamics of epidemic spreading (dynamic)
- Cancer/tumor detection
- Tissue/organ detection
- Evolution of influence (dynamic)
- Astroturfing
- Customer segmentation
- Recommendation systems
- Social network analysis (both)
- Network summarization
- Privary, group segmentation
- Link prediction (both)
- Community evolution prediction (dynamic, hot field)
<br>
<br>
## References
- [Application Areas of Community Detection: A Review : PAPER](https://ieeexplore.ieee.org/document/8625349)

Community Detection on the GPU : NOTES

This paper discusses a GPU implementation of the Louvain community detection algorithm. Louvain algorithm obtains hierachical communities as a dendrogram through modularity optimization. Given an undirected weighted graph, all vertices are first considered to be their own communities. In the first phase, each vertex greedily decides to move to the community of one of its neighbours which gives greatest increase in modularity. If moving to no neighbour's community leads to an increase in modularity, the vertex chooses to stay with its own community. This is done sequentially for all the vertices. If the total change in modularity is more than a certain threshold, this phase is repeated. Once this local moving phase is complete, all vertices have formed their first hierarchy of communities. The next phase is called the aggregation phase, where all the vertices belonging to a community are collapsed into a single super-vertex, such that edges between communities are represented as edges between respective super-vertices (edge weights are combined), and edges within each community are represented as self-loops in respective super-vertices (again, edge weights are combined). Together, the local moving and the aggregation phases constitute a stage. This super-vertex graph is then used as input fof the next stage. This process continues until the increase in modularity is below a certain threshold. As a result from each stage, we have a hierarchy of community memberships for each vertex as a dendrogram.
Approaches to perform the Louvain algorithm can be divided into coarse-grained and fine-grained. Coarse-grained approaches process a set of vertices in parallel, while fine-grained approaches process all vertices in parallel. A coarse-grained hybrid-GPU algorithm using multi GPUs has be implemented by Cheong et al. which grabbed my attention. In addition, their algorithm does not use hashing for the local moving phase, but instead sorts each neighbour list based on the community id of each vertex.
https://gist.github.com/wolfram77/7e72c9b8c18c18ab908ae76262099329

Survey for extra-child-process package : NOTES

Useful additions to inbuilt child_process module.
📦 Node.js, 📜 Files, 📰 Docs.
Please see attached PDF for literature survey.
https://gist.github.com/wolfram77/d936da570d7bf73f95d1513d4368573e

Dynamic Batch Parallel Algorithms for Updating PageRank : POSTER

This paper presents two algorithms for efficiently computing PageRank on dynamically updating graphs in a batched manner: DynamicLevelwisePR and DynamicMonolithicPR. DynamicLevelwisePR processes vertices level-by-level based on strongly connected components and avoids recomputing converged vertices on the CPU. DynamicMonolithicPR uses a full power iteration approach on the GPU that partitions vertices by in-degree and skips unaffected vertices. Evaluation on real-world graphs shows the batched algorithms provide speedups of up to 4000x over single-edge updates and outperform other state-of-the-art dynamic PageRank algorithms.

Abstract for IPDPS 2022 PhD Forum on Dynamic Batch Parallel Algorithms for Up...

For the PhD forum an abstract submission is required by 10th May, and poster by 15th May. The event is on 30th May.
https://gist.github.com/wolfram77/1c1f730d20b51e0d2c6d477fd3713024

Fast Incremental Community Detection on Dynamic Graphs : NOTES

In this paper, the authors describe two approaches for dynamic community detection using the CNM algorithm. CNM is a hierarchical, agglomerative algorithm that greedily maximizes modularity. They define two approaches: BasicDyn and FastDyn. BasicDyn backtracks merges of communities until each marked (changed) vertex is its own singleton community. FastDyn undoes a merge only if the quality of merge, as measured by the induced change in modularity, has significantly decreased compared to when the merge initially took place. FastDyn also allows more than two vertices to contract together if in the previous time step these vertices eventually ended up contracted in the same community. In the static case, merging several vertices together in one contraction phase could lead to deteriorating results. FastDyn is able to do this, however, because it uses information from the merges of the previous time step. Intuitively, merges that previously occurred are more likely to be acceptable later.
https://gist.github.com/wolfram77/1856b108334cc822cdddfdfa7334792a

Can you ﬁx farming by going back 8000 years : NOTES

1. Human population didn't explode, but plateued.
2. Fertilizer prices are going to the sky.
3. Farmers are looking for alternatives such as animal waste (manure) or even human waste.
4. Manure prices are also going up.
5. Switching to organic farming not an option.
https://gist.github.com/wolfram77/49067fc3ddc1ba2e1db4f873056fd88a

HITS algorithm : NOTES

1. Webpages tend to behave as authorities or hubs.
2. An authority represents an research thesis, and a hub represents an encyclopedia.
3. Each page has an authority and a hub score.
4. The graph is based on query, included pointed to and from pages.
5. Authority score is the sum of scores of all hubs pointing to it.
6. Hub score is the sum of scores of all authorities is pointing to.
7. Score are normalized with L2-norm in each iteration (root of sum of squares).
8. Needs to be performed at query time.
9. Two scores are returned, instead of just one.
https://gist.github.com/wolfram77/3d9ef6c5a5b63f53caabce4812c7ea81

Basic Computer Architecture and the Case for GPUs : NOTES

Computer architectures are facing issues:
Memory latencies are far higher.
Benefits from instruction level parallelism (ILP) is reducing.
With increasing clock rates, power consumption is increasing.
Increasing complexity with multi-stage pipelines, intermediate buffers, multi-level caches, out-of-order execution, branch prediction, ...
GPUs are parallel computer architectures that are good at some tasks, not so good at others. Running routines with high arithmetic intensity with overlapped memory access is the preferred approach. They may be unsuitable for irregular algorithms, where it is difficult to get high efficiency due to the high latency of accesses. They are less versatile compared to CPUs, using SIMD parallelism, and are dense compute-wise (per currency). NVIDIA's CUDA programming model enables GPUs to be used for general-purpose computing, and hence the term GPGPU.
GPU Architectural, Programming, and Performance Models presentation at PPoPP, 2010, Bangalore, India.
By Prof. Kishore Kothapalli with Prof. P. J. Narayanan and Suryakant Patidar.
https://gist.github.com/wolfram77/43a6660121eef45b78c10d4e652dad6c

About TrueTime, Spanner, Clock synchronization, CAP theorem, Two-phase lockin...

About TrueTime, Spanner, Clock synchronization, CAP theorem, Two-phase lockin...

Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...

Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...

Adjusting Bitset for graph : SHORT REPORT / NOTES

Adjusting Bitset for graph : SHORT REPORT / NOTES

Adjusting primitives for graph : SHORT REPORT / NOTES

Adjusting primitives for graph : SHORT REPORT / NOTES

Experiments with Primitive operations : SHORT REPORT / NOTES

Experiments with Primitive operations : SHORT REPORT / NOTES

PageRank Experiments : SHORT REPORT / NOTES

PageRank Experiments : SHORT REPORT / NOTES

word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings o...

word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings o...

DyGraph: A Dynamic Graph Generator and Benchmark Suite : NOTES

DyGraph: A Dynamic Graph Generator and Benchmark Suite : NOTES

Shared memory Parallelism (NOTES)

Shared memory Parallelism (NOTES)

A Dynamic Algorithm for Local Community Detection in Graphs : NOTES

A Dynamic Algorithm for Local Community Detection in Graphs : NOTES

Scalable Static and Dynamic Community Detection Using Grappolo : NOTES

Scalable Static and Dynamic Community Detection Using Grappolo : NOTES

Application Areas of Community Detection: A Review : NOTES

Application Areas of Community Detection: A Review : NOTES

Community Detection on the GPU : NOTES

Community Detection on the GPU : NOTES

Survey for extra-child-process package : NOTES

Survey for extra-child-process package : NOTES

Dynamic Batch Parallel Algorithms for Updating PageRank : POSTER

Dynamic Batch Parallel Algorithms for Updating PageRank : POSTER

Abstract for IPDPS 2022 PhD Forum on Dynamic Batch Parallel Algorithms for Up...

Abstract for IPDPS 2022 PhD Forum on Dynamic Batch Parallel Algorithms for Up...

Fast Incremental Community Detection on Dynamic Graphs : NOTES

Fast Incremental Community Detection on Dynamic Graphs : NOTES

Can you ﬁx farming by going back 8000 years : NOTES

Can you ﬁx farming by going back 8000 years : NOTES

HITS algorithm : NOTES

HITS algorithm : NOTES

Basic Computer Architecture and the Case for GPUs : NOTES

Basic Computer Architecture and the Case for GPUs : NOTES

Artificia Intellicence and XPath Extension Functions

The purpose of this presentation is to provide an overview of how you can use AI from XSLT, XQuery, Schematron, or XML Refactoring operations, the potential benefits of using AI, and some of the challenges we face.

Malibou Pitch Deck For Its €3M Seed Round

French start-up Malibou raised a €3 million Seed Round to develop its payroll and human resources
management platform for VSEs and SMEs. The financing round was led by investors Breega, Y Combinator, and FCVC.

UI5con 2024 - Bring Your Own Design System

How do you combine the OpenUI5/SAPUI5 programming model with a design system that makes its controls available as Web Components? Since OpenUI5/SAPUI5 1.120, the framework supports the integration of any Web Components. This makes it possible, for example, to natively embed own Web Components of your design system which are created with Stencil. The integration embeds the Web Components in a way that they can be used naturally in XMLViews, like with standard UI5 controls, and can be bound with data binding. Learn how you can also make use of the Web Components base class in OpenUI5/SAPUI5 to also integrate your Web Components and get inspired by the solution to generate a custom UI5 library providing the Web Components control wrappers for the native ones.

Mobile app Development Services | Drona Infotech

Drona Infotech is one of the Best Mobile App Development Company In Noida Maintenance and ongoing support. mobile app development Services can help you maintain and support your app after it has been launched. This includes fixing bugs, adding new features, and keeping your app up-to-date with the latest
Visit Us For :

Transform Your Communication with Cloud-Based IVR Solutions

Discover the power of Cloud-Based IVR Solutions to streamline communication processes. Embrace scalability and cost-efficiency while enhancing customer experiences with features like automated call routing and voice recognition. Accessible from anywhere, these solutions integrate seamlessly with existing systems, providing real-time analytics for continuous improvement. Revolutionize your communication strategy today with Cloud-Based IVR Solutions. Learn more at: https://thesmspoint.com/channel/cloud-telephony

8 Best Automated Android App Testing Tool and Framework in 2024.pdf

Regarding mobile operating systems, two major players dominate our thoughts: Android and iPhone. With Android leading the market, software development companies are focused on delivering apps compatible with this OS. Ensuring an app's functionality across various Android devices, OS versions, and hardware specifications is critical, making Android app testing essential.

Everything You Need to Know About X-Sign: The eSign Functionality of XfilesPr...

Wondering how X-Sign gained popularity in a quick time span? This eSign functionality of XfilesPro DocuPrime has many advancements to offer for Salesforce users. Explore them now!

All you need to know about Spring Boot and GraalVM

All you need to know about Spring Boot and GraalVM 🐰

Energy consumption of Database Management - Florina Jonuzi

Presentation from Florina Jonuzi at the GSD Community Stage Meetup on June 06, 2024

UI5con 2024 - Boost Your Development Experience with UI5 Tooling Extensions

The UI5 tooling is the development and build tooling of UI5. It is built in a modular and extensible way so that it can be easily extended by your needs. This session will showcase various tooling extensions which can boost your development experience by far so that you can really work offline, transpile your code in your project to use even newer versions of EcmaScript (than 2022 which is supported right now by the UI5 tooling), consume any npm package of your choice in your project, using different kind of proxies, and even stitching UI5 projects during development together to mimic your target environment.

Odoo ERP Vs. Traditional ERP Systems – A Comparative Analysis

When it is all about ERP solutions, companies typically meet their needs with common ERP solutions like SAP, Oracle, and Microsoft Dynamics. These big players have demonstrated that ERP systems can be either simple or highly comprehensive. This remains true today, but there are new factors to consider, including a promising new contender in the market that’s Odoo. This blog compares Odoo ERP with traditional ERP systems and explains why many companies now see Odoo ERP as the best choice.
What are ERP Systems?
An ERP, or Enterprise Resource Planning, system provides your company with valuable information to help you make better decisions and boost your ROI. You should choose an ERP system based on your company’s specific needs. For instance, if you run a manufacturing or retail business, you will need an ERP system that efficiently manages inventory. A consulting firm, on the other hand, would benefit from an ERP system that enhances daily operations. Similarly, eCommerce stores would select an ERP system tailored to their needs.
Because different businesses have different requirements, ERP system functionalities can vary. Among the various ERP systems available, Odoo ERP is considered one of the best in the ERp market with more than 12 million global users today.
Odoo is an open-source ERP system initially designed for small to medium-sized businesses but now suitable for a wide range of companies. Odoo offers a scalable and configurable point-of-sale management solution and allows you to create customised modules for specific industries. Odoo is gaining more popularity because it is built in a way that allows easy customisation, has a user-friendly interface, and is affordable. Here, you will cover the main differences and get to know why Odoo is gaining attention despite the many other ERP systems available in the market.

316895207-SAP-Oil-and-Gas-Downstream-Training.pptx

316895207-SAP-Oil-and-Gas-Downstream-Training.pptx

Mobile App Development Company In Noida | Drona Infotech

Drona Infotech is a premier mobile app development company in Noida, providing cutting-edge solutions for businesses.
Visit Us For : https://www.dronainfotech.com/mobile-application-development/

J-Spring 2024 - Going serverless with Quarkus, GraalVM native images and AWS ...

Presented at NLJUG's J-Spring 2024.

2024 eCommerceDays Toulouse - Sylius 2.0.pdf

Sylius 2.0 New features
Unvealing the future

GreenCode-A-VSCode-Plugin--Dario-Jurisic

Presentation about a VSCode plugin from Dario Jurisic at the GSD Community Stage meetup

Using Xen Hypervisor for Functional Safety

An update on making Xen hypervisor functionally safe and enhancing its usage in automotive and industrial use cases

E-commerce Development Services- Hornet Dynamics

For any business hoping to succeed in the digital age, having a strong online presence is crucial. We offer Ecommerce Development Services that are customized according to your business requirements and client preferences, enabling you to create a dynamic, safe, and user-friendly online store.

SQL Accounting Software Brochure Malaysia

SQL Accounting Software Brochure

SMS API Integration in Saudi Arabia| Best SMS API Service

Discover the benefits and implementation of SMS API integration in the UAE and Middle East. This comprehensive guide covers the importance of SMS messaging APIs, the advantages of bulk SMS APIs, and real-world case studies. Learn how CEQUENS, a leader in communication solutions, can help your business enhance customer engagement and streamline operations with innovative CPaaS, reliable SMS APIs, and omnichannel solutions, including WhatsApp Business. Perfect for businesses seeking to optimize their communication strategies in the digital age.

Artificia Intellicence and XPath Extension Functions

Artificia Intellicence and XPath Extension Functions

Malibou Pitch Deck For Its €3M Seed Round

Malibou Pitch Deck For Its €3M Seed Round

UI5con 2024 - Bring Your Own Design System

UI5con 2024 - Bring Your Own Design System

Mobile app Development Services | Drona Infotech

Mobile app Development Services | Drona Infotech

Transform Your Communication with Cloud-Based IVR Solutions

Transform Your Communication with Cloud-Based IVR Solutions

8 Best Automated Android App Testing Tool and Framework in 2024.pdf

8 Best Automated Android App Testing Tool and Framework in 2024.pdf

Everything You Need to Know About X-Sign: The eSign Functionality of XfilesPr...

Everything You Need to Know About X-Sign: The eSign Functionality of XfilesPr...

All you need to know about Spring Boot and GraalVM

All you need to know about Spring Boot and GraalVM

Energy consumption of Database Management - Florina Jonuzi

Energy consumption of Database Management - Florina Jonuzi

UI5con 2024 - Boost Your Development Experience with UI5 Tooling Extensions

UI5con 2024 - Boost Your Development Experience with UI5 Tooling Extensions

Odoo ERP Vs. Traditional ERP Systems – A Comparative Analysis

Odoo ERP Vs. Traditional ERP Systems – A Comparative Analysis

316895207-SAP-Oil-and-Gas-Downstream-Training.pptx

316895207-SAP-Oil-and-Gas-Downstream-Training.pptx

Mobile App Development Company In Noida | Drona Infotech

Mobile App Development Company In Noida | Drona Infotech

J-Spring 2024 - Going serverless with Quarkus, GraalVM native images and AWS ...

J-Spring 2024 - Going serverless with Quarkus, GraalVM native images and AWS ...

2024 eCommerceDays Toulouse - Sylius 2.0.pdf

2024 eCommerceDays Toulouse - Sylius 2.0.pdf

GreenCode-A-VSCode-Plugin--Dario-Jurisic

GreenCode-A-VSCode-Plugin--Dario-Jurisic

Using Xen Hypervisor for Functional Safety

Using Xen Hypervisor for Functional Safety

E-commerce Development Services- Hornet Dynamics

E-commerce Development Services- Hornet Dynamics

SQL Accounting Software Brochure Malaysia

SQL Accounting Software Brochure Malaysia

SMS API Integration in Saudi Arabia| Best SMS API Service

SMS API Integration in Saudi Arabia| Best SMS API Service

- 1. Adjusting PageRank parameters and comparing results Web graphs unaltered are reducible, and thus the rate of convergence of the power-iteration method is the rate at which αk → 0, where α is the damping factor, and k is the iteration count. An estimate of the number of iterations needed to converge to a tolerance τ is logα τ. For τ = 10-6 and α = 0.85, it can take roughly 85 iterations to converge. For α = 0.95, and α = 0.75, with the same tolerance τ = 10-6 , it takes roughly 269 and 48 iterations respectively. For τ = 10-9 , and τ = 10-3 , with the same damping factor α = 0.85, it takes roughly 128 and 43 iterations respectively. Thus, adjusting the damping factor or the tolerance parameters of the PageRank algorithm can have a significant effect on the convergence rate, both in terms of time and iterations. However, especially with the damping factor α, adjustment of the parameter value is a delicate balancing act. For smaller values of α, the convergence is fast, but the link structure of the graph used to determine ranks is less true. Slightly different values for α can produce very different rank vectors. Moreover, as α → 1, convergence slows down drastically, and sensitivity issues begin to surface [langville04]. For the first experiment, the damping factor α (which is usually 0.85) is varied from 0.50 to 1.00 in steps of 0.05. This is in order to compare the performance variation with each damping factor. The calculated error is the L1-norm with respect to default PageRank (α = 0.85). The PageRank algorithm used here is the standard power-iteration (pull) based PageRank. The rank of a vertex in an iteration is calculated as c0 + αΣrn/dn, where c0 is the common teleport contribution, α is the damping factor, rn is the previous rank of vertex with an incoming edge, dn is the out-degree of the incoming-edge vertex, and N is the total number of vertices in the graph. The common teleport contribution c0, calculated as (1-α)/N + αΣrn/N, includes the contribution due to a teleport from any vertex in the graph due to the damping factor (1-α)/N, and teleport from dangling vertices (with no outgoing edges) in the graph αΣrn/N. This is because a random surfer jumps to a random page upon visiting a page with no links, in order to avoid the rank-sink effect. All seventeen graphs used in this experiment are stored in the MatrixMarket (.mtx) file format, and obtained from the SuiteSparse Matrix Collection. These include: web-Stanford, web-BerkStan, web-Google, web-NotreDame, soc-Slashdot0811, soc-Slashdot0902, soc-Epinions1, coAuthorsDBLP, coAuthorsCiteseer, soc-LiveJournal1, coPapersCiteseer, coPapersDBLP, indochina-2004, italy_osm, great-britain_osm, germany_osm, asia_osm. The experiment is implemented in C++, and compiled using GCC 9 with optimization level 3 (-O3). The system used is a Dell PowerEdge R740 Rack server with two Intel Xeon Silver 4116 CPUs @ 2.10GHz, 128GB DIMM DDR4 Synchronous Registered (Buffered) 2666 MHz (8x16GB) DRAM, and running CentOS Linux release 7.9.2009 (Core). The iterations taken with each test case is measured. 500 is the maximum iterations allowed. Statistics of each test case is printed to standard output (stdout), and redirected to a log file, which is then processed with a script to generate a CSV file, with each row representing the details of a single test case. This CSV file is imported into Google Sheets, and necessary tables are set up with the help of the FILTER function to create the charts. When comparing the relative performance of different approaches with multiple test graphs, there are two ways to obtain an average comparison: relative-average, and average-relative.
- 2. A relative-average comparison first finds relative performance (ratio) of each approach with respect to a baseline approach (one of them), and then averages them. Consider, for example, three approaches a, b, and c, with 3 test runs for each of the three approaches, labeled a1, a2, a3, b1, b2, b3, c1, c2, c3. The relative performance of each approach with respect to c would be a1/c1, b1/c1, c1/c1, a2/c2, b2/c2, and so on. The relative-average comparison is now the average of these ratios, i.e., (a1/c1+a2/c2+a3/c3)/3 for a, (b1/c1+b2/c2+b3/c3)/3, and 1 for c. In contrast, an average-relative comparison first finds the average time/iterations taken for each approach with respect to a baseline approach, and then finds the relative performance. Again, considering three approaches, with 3 test runs as above, the average values of each approach would be (a1+a2+a3)/3 for a, (b1+b2+b3)/3 for b, and (c1+c2+c3)/3 for c. The average-relative comparison of each approach with respect to c would then be (a1+a2+a3)/(c1+c2+c3) for a, (b1+b2+b3)/(c1+c2+c3) for b, and 1 for c. Semantically, a relative-average comparison gives equal importance to the relative performance of each test run (graph), while an average-relative comparison gives equal importance to magnitude (time/iterations) of all test runs (or simply, it gives higher importance to test runs with larger graphs). For these experiments, both comparisons are made, but only one of them is presented here if they are quite similar. Figure 1: Average iterations for PageRank computation with damping factor α adjusted from 0.50 - 1.00 in steps of 0.05. Charts for relative-average, and average-relative iterations (with respect to damping factor α = 0.85) follow the same curve, but with different values (values for relative-average and average-relative iterations are quite similar). Results (figure 1) indicate that increasing the damping factor α beyond 0.85 significantly increases convergence time, and lowering it below 0.85 decreases convergence time. On average, using a damping factor α = 0.95 increases both convergence time and iterations by 192%, and using a damping factor α = 0.75 decreases both by 41% (compared to damping
- 3. factor α = 0.85). Note that a higher damping factor implies that a random surfer follows links with higher probability (and jumps to a random page with lower probability). Observing that adjusting the damping factor has a significant effect, another experiment was performed. The idea behind this experiment was to adjust the damping factor α in steps, to see if it might help reduce PageRank computation time. The PageRank computation first starts with a small α, changes it when ranks have converged, until the final desired value of α. For example, the computation starts initially with α = 0.5, lets ranks converge quickly, and then switches to α = 0.85 and continues PageRank computation until it converges. This single-step change is attempted with the initial (fast converge) damping factor α from 0.1 to 0.84. Similar to this, two-step, three-step, and four-step changes are also attempted. With a two-step approach, a midpoint between the damping_start value and 0.85 is selected as well for the second set of iterations. Similarly, three-step and four-step approaches use two and three midpoints respectively. A small sample graph is used in this experiment, which is stored in the MatrixMarket (.mtx) file format. The experiment is implemented in Node.js, and executed on a personal laptop. Only the iteration count of each test case is measured. The tolerance τ = 10-5 is used for all test cases. Statistics of each test case is printed to standard output (stdout), and redirected to a log file, which is then processed with a script to generate a CSV file, with each row representing the details of a single test case. This CSV file is imported into Google Sheets, and necessary tables are set up with the help of the FILTER function to create the charts. Figure 2: Iterations required for PageRank computation, when damping factor α is adjusted in 1-4 steps, starting with damping_start. 0-step is the fixed damping factor PageRank, with α = 0.85.
- 4. From the results (figure 2), it is clear that modifying the damping factor α in steps is not a good idea. The standard fixed damping factor PageRank, with α = 0.85, converges in 35 iterations. Using a single step approach increases the number of iterations required, which further increases as the initial damping factor damping_start is increased. Switching to a multi-step approach also increases the number of iterations needed for convergence. A possible explanation for this effect is that the ranks for different values of the damping factor α are significantly different, and switching to a different damping factor α after each step mostly leads to recomputation. Similar to the damping factor α, adjusting the value of tolerance τ can have a significant effect as well. Apart from the value of tolerance τ, it is observed that different people make use of different error functions for measuring tolerance. Although L1 norm is commonly used for convergence check, it appears nvGraph uses L2 norm instead [nvgraph]. Another person in stackoverflow seems to suggest the use of per-vertex tolerance comparison, which is essentially the L∞ norm. The L1 norm ||E||1 between two (rank) vectors r and s is calculated as ||E||1 = Σ|rn - sn|, or as the sum of absolute errors. The L2 norm ||E||2 is calculated as ||E||2 = √Σ|rn - sn|2 , or as the square-root of the sum of squared errors (euclidean distance between the two vectors). The L∞ norm ||E||∞ is calculated as ||E||∞ = max(|rn - sn|), or as the maximum of absolute errors. This experiment was for comparing the performance between PageRank computation with L1, L2 and L∞ norms as convergence check, for various tolerance τ values ranging from 10-0 to 10-10 (10-0 , 5×10-0 , 10-1 , 5×10-1 , ...). The input graphs, system used, and the rest of the experimental process is similar to that of the first experiment. tolerance L1 norm L2 norm L∞ norm 1.00E-05 49 65 27 5.00E-06 53 65 31 1.00E-06 63 500 41 5.00E-07 67 500 45 1.00E-07 77 500 55 5.00E-08 84 500 59 1.00E-08 500 500 70 5.00E-09 500 500 73 1.00E-09 500 500 500 5.00E-10 500 500 500 1.00E-10 500 500 500 Table 1: Iterations taken for PageRank computation of the web-Stanford graph, with L1, L2, and L∞ norms used as convergence check. At tolerance τ = 10-6 , the L2 norm suffers from sensitivity issues, followed by L1 and L∞ norms at 10-8 and 10-9 respectively. Only relevant tolerances are shown here.
- 5. Figure 3: Iterations taken for PageRank computation of the asia_osm graph, with L1, L2, and L∞ norms used as convergence check. Until tolerance τ = 10-7 , the L∞ norm converges in just one iteration. Figure 4: Average iterations taken for PageRank computation with L1, L2 and L∞ norms as convergence check, and tolerance τ adjusted from 10-0 to 10-10 (10-0 , 5×10-0 , 10-1 , 5×10-1 , ...). L∞ norm convergence check seems to be the fastest, followed by L1 norm (on average).
- 6. Figure 5: Average-relative iterations taken for PageRank computation with L1, L2 and L∞ norms as convergence check, and tolerance τ adjusted from 10-0 . L∞ norm convergence check seems to be the fastest, however, it is difficult to tell whether L1, or L2 norm comes in seconds place (on average). Figure 6: Relative-average iterations taken for PageRank computation with L1, L2 and L∞ norms as convergence check, and tolerance τ adjusted from 10-0 . L∞ norm convergence check seems to be the fastest, followed by L2 norm (on average).
- 7. For various graphs, it is observed that PageRank computation with L1, L2, or L∞ norm as convergence check suffers from sensitivity issues beyond certain (smaller) tolerance τ values. As tolerance τ is decreased from 10-0 to 10-10 , L2 norm is usually (except road networks) the first to suffer from this issue, followed by L1 norm (or L2), and eventually L∞ norm (if ever). This sensitivity issue was recognized by the fact that a given approach abruptly takes 500 (max iterations) for the next lower tolerance τ value. This is shown in table 1. It is also observed that PageRank computation with L∞ norm as convergence check completes in just one iteration (even for tolerance τ ≥ 10-6 ) for large graphs (road networks). This is because it is calculated as ||E||∞ = max(|rn - sn|), and depending upon the order (number of vertices) N of the graph, 1/N can be less than the required tolerance τ to converge. Based on average-relative comparison, the relative iterations between PageRank computation with L1, L2, and L∞ norm as convergence check is 4.73 : 4.08 : 1.00. Hence L2 norm is on average 16% faster than L1 norm, and L∞ norm is 308% faster (~4x) than L2 norm. The variation of average-relative iterations for various tolerance τ values is shown in figure 5. A similar effect is also seen in figure 4, where average iterations for various tolerance τ values is shown. On the other hand, based on relative-average comparison, the relative iterations between PageRank computation with L1, L2, and L∞ norm as convergence check is 10.42 : 6.18 : 1. Hence, L2 norm is on average 69% faster than L1 norm, and L∞ norm is 518% faster (~6x) than L2 norm. The variation of relative-average iterations for various tolerance τ values is shown in figure 6. This shows that while L1 norm is on average slower than L2 norm, the difference between the two diminishes for large graphs (average-relative comparison gives higher importance to results from larger graphs, unlike relative-average). It should also be noted that L2 norm is not always faster than L1 norm in several cases (usually for smaller tolerance τ values) as can be seen in table 1. Parameter values can have a significant effect on performance, as seen in these experiments. Different convergence functions converge at different rates, and which of them converges faster depends upon the tolerance τ value. Iteration count needs to be checked in order to ensure that no approach is suffering from sensitivity issues, or is leading to a single iteration convergence. Finally, the relative performance comparison method affects which results get more importance, and which do not, in the final average. Taking note of each of these points, when comparing iterative algorithms, will thus ensure that the performance results are accurate and useful. Table 2: List of parameter adjustment strategies, and links to source code. Damping Factor adjust dynamic-adjust Tolerance L1 norm L2 norm L∞ norm 1. Comparing the effect of using different values of damping factor, with PageRank (pull, CSR). 2. Experimenting PageRank improvement by adjusting damping factor (α) between iterations. 3. Comparing the effect of using different functions for convergence check, with PageRank (...). 4. Comparing the effect of using different values of tolerance, with PageRank (pull, CSR).