Principal Component Analysis, or PCA, is a factual method that permits you to sum up the data contained in enormous information tables by methods for a littler arrangement of "synopsis files" that can be all the more handily envisioned and broke down.
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
Process of converting data set having vast dimensions into data set with lesser dimensions ensuring that it conveys similar information concisely.
Concept
R code
Influence over the Dimensionality Reduction and Clustering for Air Quality Me...IJAEMSJORNAL
The current trend in the industry is to analyze large data sets and apply data mining, machine learning techniques to identify a pattern. But the challenges with huge data sets are the high dimensions associated with it. Sometimes in data analytics applications, large amounts of data produce worse performance. Also, most of the data mining algorithms are implemented column wise and too many columns restrict the performance and make it slower. Therefore, dimensionality reduction is an important step in data analysis. Dimensionality reduction is a technique that converts high dimensional data into much lower dimension, such that maximum variance is explained within the first few dimensions. This paper focuses on multivariate statistical and artificial neural networks techniques for data reduction. Each method has a different rationale to preserve the relationship between input parameters during analysis. Principal Component Analysis which is a multivariate technique and Self Organising Map a neural network technique is presented in this paper. Also, a hierarchical clustering approach has been applied to the reduced data set. A case study of Air quality measurement has been considered to evaluate the performance of the proposed techniques.
Bank - Loan Purchase Modeling
This case is about a bank which has a growing customer base. Majority of these customers are liability customers (depositors) with varying size of deposits. The number of customers who are also borrowers (asset customers) is quite small, and the bank is interested in expanding this base rapidly to bring in more loan business and in the process, earn more through the interest on loans. In particular, the management wants to explore ways of converting its liability customers to personal loan customers (while retaining them as depositors). A campaign that the bank ran last year for liability customers showed a healthy conversion rate of over 9% success. This has encouraged the retail marketing department to devise campaigns with better target marketing to increase the success ratio with a minimal budget. The department wants to build a model that will help them identify the potential customers who have a higher probability of purchasing the loan. This will increase the success ratio while at the same time reduce the cost of the campaign. The dataset has data on 5000 customers. The data include customer demographic information (age, income, etc.), the customer's relationship with the bank (mortgage, securities account, etc.), and the customer response to the last personal loan campaign (Personal Loan). Among these 5000 customers, only 480 (= 9.6%) accepted the personal loan that was offered to them in the earlier campaign.
Our job is to build the best model which can classify the right customers who have a higher probability of purchasing the loan. We are expected to do the following:
EDA of the data available. Showcase the results using appropriate graphs
Apply appropriate clustering on the data and interpret the output .
Build appropriate models on both the test and train data (CART & Random Forest). Interpret all the model outputs and do the necessary modifications wherever eligible (such as pruning).
Check the performance of all the models that you have built (test and train). Use all the model performance measures you have learned so far. Share your remarks on which model performs the best.
Principal Component Analysis, or PCA, is a factual method that permits you to sum up the data contained in enormous information tables by methods for a littler arrangement of "synopsis files" that can be all the more handily envisioned and broke down.
Principal Component Analysis and ClusteringUsha Vijay
Identifying the borrower segments from the give bank data set which has 27000 rows and 77 variable using PROC PRINCOMP. variables, it is important to reduce the data set to a smaller set of variables to derive a feasible
conclusion. With the effect of multicollinearity two or more variables can share the same plane in the in dimensions. Each row of the data can
be envisioned as a 77 dimensional graph and when we project the data as orthonormal, it is expected that the certain characteristics of the
data based on the plots to cluster together as principal components. In order to identify these principal components. PROC PRINCOMP is
executed with all the variables except the constant variables(recoveries and collection fees) and we derive a plot of Eigen values of all the
principal components
Process of converting data set having vast dimensions into data set with lesser dimensions ensuring that it conveys similar information concisely.
Concept
R code
Influence over the Dimensionality Reduction and Clustering for Air Quality Me...IJAEMSJORNAL
The current trend in the industry is to analyze large data sets and apply data mining, machine learning techniques to identify a pattern. But the challenges with huge data sets are the high dimensions associated with it. Sometimes in data analytics applications, large amounts of data produce worse performance. Also, most of the data mining algorithms are implemented column wise and too many columns restrict the performance and make it slower. Therefore, dimensionality reduction is an important step in data analysis. Dimensionality reduction is a technique that converts high dimensional data into much lower dimension, such that maximum variance is explained within the first few dimensions. This paper focuses on multivariate statistical and artificial neural networks techniques for data reduction. Each method has a different rationale to preserve the relationship between input parameters during analysis. Principal Component Analysis which is a multivariate technique and Self Organising Map a neural network technique is presented in this paper. Also, a hierarchical clustering approach has been applied to the reduced data set. A case study of Air quality measurement has been considered to evaluate the performance of the proposed techniques.
Bank - Loan Purchase Modeling
This case is about a bank which has a growing customer base. Majority of these customers are liability customers (depositors) with varying size of deposits. The number of customers who are also borrowers (asset customers) is quite small, and the bank is interested in expanding this base rapidly to bring in more loan business and in the process, earn more through the interest on loans. In particular, the management wants to explore ways of converting its liability customers to personal loan customers (while retaining them as depositors). A campaign that the bank ran last year for liability customers showed a healthy conversion rate of over 9% success. This has encouraged the retail marketing department to devise campaigns with better target marketing to increase the success ratio with a minimal budget. The department wants to build a model that will help them identify the potential customers who have a higher probability of purchasing the loan. This will increase the success ratio while at the same time reduce the cost of the campaign. The dataset has data on 5000 customers. The data include customer demographic information (age, income, etc.), the customer's relationship with the bank (mortgage, securities account, etc.), and the customer response to the last personal loan campaign (Personal Loan). Among these 5000 customers, only 480 (= 9.6%) accepted the personal loan that was offered to them in the earlier campaign.
Our job is to build the best model which can classify the right customers who have a higher probability of purchasing the loan. We are expected to do the following:
EDA of the data available. Showcase the results using appropriate graphs
Apply appropriate clustering on the data and interpret the output .
Build appropriate models on both the test and train data (CART & Random Forest). Interpret all the model outputs and do the necessary modifications wherever eligible (such as pruning).
Check the performance of all the models that you have built (test and train). Use all the model performance measures you have learned so far. Share your remarks on which model performs the best.
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
Data Science - Part VII - Cluster AnalysisDerek Kane
This lecture provides an overview of clustering techniques, including K-Means, Hierarchical Clustering, and Gaussian Mixed Models. We will go through some methods of calibration and diagnostics and then apply the technique on a recognizable dataset.
COMPARISION OF PERCENTAGE ERROR BY USING IMPUTATION METHOD ON MID TERM EXAMIN...ijiert bestjournal
The issue of incomplete data exists across the enti re field of data mining. In this paper,Mean Imputation,Median Imputation and Standard Dev iation Imputation are used to deal with challenges of incomplete data on classifi cation problems. By using different imputation methods converts incomplete dataset in t o the complete dataset. On complete dataset by applying the suitable Imputatio n Method and comparing the percentage error of Imputation Method and comparing the result
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
Data Science - Part VII - Cluster AnalysisDerek Kane
This lecture provides an overview of clustering techniques, including K-Means, Hierarchical Clustering, and Gaussian Mixed Models. We will go through some methods of calibration and diagnostics and then apply the technique on a recognizable dataset.
COMPARISION OF PERCENTAGE ERROR BY USING IMPUTATION METHOD ON MID TERM EXAMIN...ijiert bestjournal
The issue of incomplete data exists across the enti re field of data mining. In this paper,Mean Imputation,Median Imputation and Standard Dev iation Imputation are used to deal with challenges of incomplete data on classifi cation problems. By using different imputation methods converts incomplete dataset in t o the complete dataset. On complete dataset by applying the suitable Imputatio n Method and comparing the percentage error of Imputation Method and comparing the result
A short presentation for beginners on Introduction of Machine Learning, What it is, how it works, what all are the popular Machine Learning techniques and learning models (supervised, unsupervised, semi-supervised, reinforcement learning) and how they works with various Industry use-cases and popular examples.
Suggestions:
1) For best quality, download the PDF before viewing.
2) Open at least two windows: One for the Youtube video, one for the screencast (link below), and optionally one for the slides themselves.
3) The Youtube video is shown on the first page of the slide deck, for slides, just skip to page 2.
Screencast: http://youtu.be/VoL7JKJmr2I
Video recording: http://youtu.be/CJRvb8zxRdE (Thanks to Al Friedrich!)
In this talk, we take Deep Learning to task with real world data puzzles to solve.
Data:
- Higgs binary classification dataset (10M rows, 29 cols)
- MNIST 10-class dataset
- Weather categorical dataset
- eBay text classification dataset (8500 cols, 500k rows, 467 classes)
- ECG heartbeat anomaly detection
- Powered by the open source machine learning software H2O.ai. Contributors welcome at: https://github.com/h2oai
- To view videos on H2O open source machine learning software, go to: https://www.youtube.com/user/0xdata
In the present day huge amount of data is generated in every minute and transferred frequently. Although
the data is sometimes static but most commonly it is dynamic and transactional. New data that is being
generated is getting constantly added to the old/existing data. To discover the knowledge from this
incremental data, one approach is to run the algorithm repeatedly for the modified data sets which is time
consuming. Again to analyze the datasets properly, construction of efficient classifier model is necessary.
The objective of developing such a classifier is to classify unlabeled dataset into appropriate classes. The
paper proposes a dimension reduction algorithm that can be applied in dynamic environment for
generation of reduced attribute set as dynamic reduct, and an optimization algorithm which uses the
reduct and build up the corresponding classification system. The method analyzes the new dataset, when it
becomes available, and modifies the reduct accordingly to fit the entire dataset and from the entire data
set, interesting optimal classification rule sets are generated. The concepts of discernibility relation,
attribute dependency and attribute significance of Rough Set Theory are integrated for the generation of
dynamic reduct set, and optimal classification rules are selected using PSO method, which not only
reduces the complexity but also helps to achieve higher accuracy of the decision system. The proposed
method has been applied on some benchmark dataset collected from the UCI repository and dynamic
reduct is computed, and from the reduct optimal classification rules are also generated. Experimental
result shows the efficiency of the proposed method.
High dimensionality reduction on graphical dataeSAT Journals
Abstract In spite of the fact that graph embedding has been an intense instrument for displaying data natural structures, just utilizing all elements for data structures revelation may bring about noise amplification. This is especially serious for high dimensional data with little examples. To meet this test, a novel effective structure to perform highlight determination for graph embedding, in which a classification of graph implanting routines is given a role as a slightest squares relapse issue. In this structure, a twofold component selector is acquainted with normally handle the component cardinality at all squares detailing. The proposed strategy is quick and memory proficient. The proposed system is connected to a few graph embedding learning issues, counting administered, unsupervised and semi supervised graph embedding. Key Words:Efficient feature selection, High dimensional data, Sparse graph embedding, Sparse principal component analysis, Subproblem Optimization.
Survey on Supervised Method for Face Image Retrieval Based on Euclidean Dist...Editor IJCATR
Content-based image retrieval is a technique which uses visual contents to search images from large scale image databases
according to users' interests. Given a query face image, content-based face image retrieval tries to find similar face images from a large
image database. Initially face of the image is detected from the query image. After the removal of noise present in the image, it is
separated as patches. For each patch, the Local binary pattern (LBP) is extracted which improves the detection performance. LBP is a
type of feature used for classification in computer vision. The LBP operator assigns a label to every pixel of a gray level image. The
label mapping to a pixel is affected by the relationship between this pixel and its eight neighbors. Support Vector Machine (SVM) is
used then which will produce a model (based on the training data) that predicts the target values of the test data given only the test data
attributes. When the feature values are provided to the SVM classifier, it will train about the feature. Finally it will classify about the
result. SVM maps input vectors to a higher dimensional vector space where an optimal hyper plane is constructed. Among the
available hyper planes, there is one hyper plane alone that maximizes the distance between itself and the nearest data vectors of each
category. The Euclidean distance between the query image and database image is calculated and the index of the Euclidean distance is
sorted.The indexing scheme used for this purpose provides an efficient way to search the image. Then the corresponding image from
the database is retrieved based upon the index. This SVM classifier mainly improves the detection performance and the rate of
accuracy.
Performance Comparision of Machine Learning AlgorithmsDinusha Dilanka
In this paper Compare the performance of two
classification algorithm. I t is useful to differentiate
algorithms based on computational performance rather
than classification accuracy alone. As although
classification accuracy between the algorithms is similar,
computational performance can differ significantly and it
can affect to the final results. So the objective of this paper
is to perform a comparative analysis of two machine
learning algorithms namely, K Nearest neighbor,
classification and Logistic Regression. In this paper it
was considered a large dataset of 7981 data points and 112
features. Then the performance of the above mentioned
machine learning algorithms are examined. In this paper
the processing time and accuracy of the different machine
learning techniques are being estimated by considering the
collected data set, over a 60% for train and remaining
40% for testing. The paper is organized as follows. In
Section I, introduction and background analysis of the
research is included and in section II, problem statement.
In Section III, our application and data analyze Process,
the testing environment, and the Methodology of our
analysis are being described briefly. Section IV comprises
the results of two algorithms. Finally, the paper concludes
with a discussion of future directions for research by
eliminating the problems existing with the current
research methodology.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
1. TECHNIQUES FOR BIG DATA
FEATURE EXTRACTION USING
DISTANCE COVARIANCE
BASED PCA
2. Big Data
Big Data' is a blanket term for any collection of data
sets so large and complex that it becomes difficult to
process using on-hand database management tools or
traditional data processing applications.
Big data requires exceptional technologies to efficiently
process large quantities of data within tolerable
elapsed times. A 2011 McKinsey report suggests
suitable technologies include crowdsourcing, data fusion
and integration, genetic algorithms, machine learning,
natural language processing, signal processing,
simulation, time series analysis and visualization.
3. How Big is Big Data?
Very large, distributed aggregations of loosely structured data – often
incomplete and inaccessible.
Petabytes/exabytes of data Millions/billions of people Billions/trillions of
records.
Loosely-structured and often distributed data.
Flat schemas with few complex interrelationships
Often involving time-stamped events
Often made up of incomplete data
Often including connections between data elements that must be
probabilistically inferred.
Applications that involved Big-data can be: Transactional (e.g., Facebook,
PhotoBox), or, Analytic (e.g., ClickFox, Merced Applications).
(Reference Wikibon.org)
4. Big Data
Big Data Can be of three types:
1. Large number of attributes (>16)
2. Large number of samples
3. Large number both of attributes and samples
I have tried to work on the first case.
5. What is Dimensionality Reduction?
Dimensionality reduction or dimension reduction
is the process of reducing the number of random
variables under consideration (or attributes or
features or descriptors), and can be divided into
feature selection and feature extraction.
6. Feature Selection
Filters: Pearson’s Correlation
Wrappers: Run a classifier again and again, each
time with a new set of features selected using
backward selection or forward selection.
7. Feature Extraction
Feature extraction transforms the data in the high-
dimensional space to a space of fewer dimensions.
The data transformation may be linear, as in
principal component analysis (PCA), but many
nonlinear dimensionality reduction techniques also
exist. For multidimensional data, tensor
representation can be used in dimensionality
reduction through multilinear subspace learning.
8. Feature Extraction
The main linear technique for dimensionality
reduction, principal component analysis, performs a
linear mapping of the data to a lower-dimensional
space in such a way that the variance of the data in
the low-dimensional representation is maximized
9. What is Principal Component Analysis?
Principal component analysis (PCA) is a statistical procedure that
uses an orthogonal transformation to convert a set of observations
of possibly correlated variables into a set of values of linearly
uncorrelated variables called principal components. The number of
principal components is less than or equal to the number of original
variables. This transformation is defined in such a way that the first
principal component has the largest possible variance (that is,
accounts for as much of the variability in the data as possible), and
each succeeding component in turn has the highest variance possible
under the constraint that it is orthogonal to (i.e., uncorrelated with)
the preceding components. Principal components are guaranteed to
be independent if the data set is jointly normally distributed. PCA is
sensitive to the relative scaling of the original variables.
10. That is fine, but show me the MATH!
Online tutorial
(http://www.cs.otago.ac.nz/cosc453/student_tutori
als/principal_components.pdf)
11. PCA and BIG DATA
BIG DATA containing thousands will require a lot of
computation time for an average computer.
PCA becomes an important tool while drawing
inference from such large data sets.
12. What is Distance Correlation?
Distance correlation is a measure of statistical
dependence between two random variables or two
random vectors of arbitrary, not necessarily equal
dimension. An important property is that this measure of
dependence is zero if and only if the random variables
are statistically independent. This measure is derived
from a number of other quantities that are used in its
specification, specifically: distance variance, distance
standard deviation and distance covariance. These
take the same roles as the ordinary moments with
corresponding names in the specification of the Pearson
product-moment correlation coefficient.
19. Distance Covariance Principal
Component Analysis
After we have obtained distance covariance, we
can find the highest eigen vectors of the covariance
matrix and then use those eigen vectors to extract
new features
These eigen vectors can be multiplied by the real
dataset to generate the reduced dataset.
20. PCA vs D-PCA
The classical measure of dependence, the Pearson
correlation coefficient, is mainly sensitive to a linear
relationship between two variables. Distance correlation
was introduced in 2005 by Gabor J Szekely in several
lectures to address this deficiency of Pearson’s
correlation, namely that it can easily be zero for
dependent variables. Correlation = 0
(uncorrelatedness) does not imply independence while
distance correlation = 0 does imply independence. The
first results on distance correlation were published in
2007 and 2009.
22. Modifications of D-PCA
1. pow((ai^2 – aj^2),0.5)/ai+aj
2. pow((ai^2 – aj^2),0.5)/ai
These modification can be used to scale the data
which can then eliminate Normalization Step.