This is a short report of the paper "Efficient Estimation for High Similarities using Odd Sketches" produced for the course Softskills seminar at Telecom Paristech
Dijkstra's algorithm is a graph search algorithm that finds the shortest paths between nodes in a graph. It was developed by computer scientist Edsger Dijkstra in 1956. The algorithm works by assigning tentative distances to nodes in the graph and updating them until it determines the shortest path from the starting node to all other nodes. It can be used to find optimal routes between locations on a map by treating locations as nodes and distances between them as edge costs. ArcGIS Network Analysis software uses Dijkstra's algorithm to solve network problems like finding the lowest cost route, service areas, and closest facilities.
A new text encryption algorithm which is based upon a combination between Self-Synchronizing Stream Cipher and chaotic map has been proposed in this paper. The new algorithm encrypts and decrypts text files of different sizes. First of all, the corresponding ASCII values of the plain text are served as input to the permutation operation which diffuses the positions of these values by using hyper-chaotic map. Secondly, the result values are input to substitution operation via1D Bernoulli map. Finally, the resultant vales are XOR feedback with the key.The proposed algorithm has been analyzed using a number of tests and the results show that it has large key space, a uniform histogram, low correlation and it is very sensitive to any change in the plain text or key.
This document discusses shortest path algorithms. It begins with the Konigsberg bridge problem solved by Euler that helped develop graph theory. It then discusses the shortest path problem in graph theory and two algorithms to solve it: Dijkstra's algorithm and the A* search algorithm. It explains how these algorithms work and their applications, such as in map routing, network routing, games development, and more.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
S6 l04 analytical and numerical methods of structural analysisShaikh Mohsin
This document provides an overview of analytical and numerical methods for structural analysis. It begins by explaining the process of structural analysis from the real object to the design model. It then discusses analytical methods like mechanics of materials and numerical methods like the finite element method. The document provides examples comparing analytical and numerical solutions. In summary, it outlines the appropriate uses of both methods and emphasizes the importance of understanding the underlying mechanics rather than solely relying on software tools.
Numerical Methods in Mechanical Engineering - Final ProjectStasik Nemirovsky
Final Project for the class of "Numerical Methods in Mechanical Engineering" - MECH 309.
In this project, various engineering problems were analyzed and solved using advanced numerical approximation methods and MATLAB software.
Using several mathematical examples from three different authors in texts from different courses this paper illustrates the easier way to avoid confusions and always get the correct results with the least effort was to use the proposed Excel Gamma function explained in detail for the proper use of the Q(z) and ercf(x) functions in most communication courses. The paper serves as a tutorial and introduction for such functions
This document describes techniques for object detection in images using Matlab. It detects multiple objects of different colors and shapes against a background. The key steps are:
1. Applying thresholding techniques like global, local, and adaptive thresholding to isolate objects from the background. Noise is also filtered out.
2. Using bounding boxes to find the center and boundaries of objects. Circular objects are detected by finding centers and radii.
3. Objects are counted using a simple counting program. The number of circular objects is also counted.
4. Green circular objects are isolated by identifying pixels within a specified RGB value range and applying a mask.
Dijkstra's algorithm is a graph search algorithm that finds the shortest paths between nodes in a graph. It was developed by computer scientist Edsger Dijkstra in 1956. The algorithm works by assigning tentative distances to nodes in the graph and updating them until it determines the shortest path from the starting node to all other nodes. It can be used to find optimal routes between locations on a map by treating locations as nodes and distances between them as edge costs. ArcGIS Network Analysis software uses Dijkstra's algorithm to solve network problems like finding the lowest cost route, service areas, and closest facilities.
A new text encryption algorithm which is based upon a combination between Self-Synchronizing Stream Cipher and chaotic map has been proposed in this paper. The new algorithm encrypts and decrypts text files of different sizes. First of all, the corresponding ASCII values of the plain text are served as input to the permutation operation which diffuses the positions of these values by using hyper-chaotic map. Secondly, the result values are input to substitution operation via1D Bernoulli map. Finally, the resultant vales are XOR feedback with the key.The proposed algorithm has been analyzed using a number of tests and the results show that it has large key space, a uniform histogram, low correlation and it is very sensitive to any change in the plain text or key.
This document discusses shortest path algorithms. It begins with the Konigsberg bridge problem solved by Euler that helped develop graph theory. It then discusses the shortest path problem in graph theory and two algorithms to solve it: Dijkstra's algorithm and the A* search algorithm. It explains how these algorithms work and their applications, such as in map routing, network routing, games development, and more.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
S6 l04 analytical and numerical methods of structural analysisShaikh Mohsin
This document provides an overview of analytical and numerical methods for structural analysis. It begins by explaining the process of structural analysis from the real object to the design model. It then discusses analytical methods like mechanics of materials and numerical methods like the finite element method. The document provides examples comparing analytical and numerical solutions. In summary, it outlines the appropriate uses of both methods and emphasizes the importance of understanding the underlying mechanics rather than solely relying on software tools.
Numerical Methods in Mechanical Engineering - Final ProjectStasik Nemirovsky
Final Project for the class of "Numerical Methods in Mechanical Engineering" - MECH 309.
In this project, various engineering problems were analyzed and solved using advanced numerical approximation methods and MATLAB software.
Using several mathematical examples from three different authors in texts from different courses this paper illustrates the easier way to avoid confusions and always get the correct results with the least effort was to use the proposed Excel Gamma function explained in detail for the proper use of the Q(z) and ercf(x) functions in most communication courses. The paper serves as a tutorial and introduction for such functions
This document describes techniques for object detection in images using Matlab. It detects multiple objects of different colors and shapes against a background. The key steps are:
1. Applying thresholding techniques like global, local, and adaptive thresholding to isolate objects from the background. Noise is also filtered out.
2. Using bounding boxes to find the center and boundaries of objects. Circular objects are detected by finding centers and radii.
3. Objects are counted using a simple counting program. The number of circular objects is also counted.
4. Green circular objects are isolated by identifying pixels within a specified RGB value range and applying a mask.
This document describes a quadratic assignment problem (QAP) involving assigning 358 constraints and 50 variables. It provides an example of a QAP with 3 facilities and 3 locations. The QAP aims to assign facilities to locations in a way that minimizes total cost, which is a function of the flow between facilities and the distance between locations. Several applications of QAP are discussed, including facility location, scheduling, and ergonomic design problems.
The document discusses different clustering algorithms, including k-means and EM clustering. K-means aims to partition items into k clusters such that each item belongs to the cluster with the nearest mean. It works iteratively to assign items to centroids and recompute centroids until the clusters no longer change. EM clustering generalizes k-means by computing probabilities of cluster membership based on probability distributions, with the goal of maximizing the overall probability of items given the clusters. Both algorithms are used to group similar items in applications like market segmentation.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
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.
Dijkstra's algorithm is a solution to the single-source shortest path problem in graph theory. It finds the shortest paths from a source vertex to all other vertices in a weighted graph where all edge weights are non-negative. The algorithm uses a greedy approach, maintaining a set of vertices whose final shortest path from the source vertex has already been determined.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
Optics ordering points to identify the clustering structureRajesh Piryani
The presentation summarized the OPTICS (Ordering Points To Identify the Clustering Structure) algorithm, a density-based clustering algorithm that addresses some limitations of DBSCAN. OPTICS does not produce an explicit clustering but instead outputs an ordering of all objects based on their reachability distances, representing the intrinsic clustering structure. It works by iteratively expanding clusters and updating an ordering seeds list to generate the output ordering without requiring pre-specification of parameters like DBSCAN. The ordering can then be used to extract clusters for a range of density parameter values. An example applying OPTICS on a 2D dataset was provided to illustrate the algorithm.
The document discusses clustering techniques and provides details about the k-means clustering algorithm. It begins with an introduction to clustering and lists different clustering techniques. It then describes the k-means algorithm in detail, including how it works, the steps involved, and provides an example illustration. Finally, it discusses comments on the k-means algorithm, focusing on aspects like choosing the value of k, initializing cluster centroids, and different distance measurement methods.
This document provides an overview of representing graphs and Dijkstra's algorithm in Prolog. It discusses different ways to represent graphs in Prolog, including using edge clauses, a graph term, and an adjacency list. It then explains Dijkstra's algorithm for finding the shortest path between nodes in a graph and provides pseudocode for implementing it in Prolog using rules for operations like finding the minimum value and merging lists.
Dijkstra's algorithm finds the shortest path from a starting node to all other nodes in a graph. It does this by examining all possible paths from the starting node and progressively eliminating longer paths, until arriving at the shortest path to each node. Flooding is a simple routing algorithm where every incoming packet is sent through every outgoing link except the one it arrived on, ensuring delivery but wasting bandwidth through duplicate packets circulating forever without precautions.
Dijkstra's algorithm allows finding the shortest path between any two vertices in a graph. It works by overestimating the distance of each vertex from the starting point and then visiting neighbors to find shorter paths. The algorithm uses a greedy approach, finding the next best solution at each step. It maintains path distances in an array and maps each vertex to its predecessor in the shortest path. A priority queue is used to efficiently retrieve the closest vertex. The time complexity is O(E Log V) and space is O(V). Applications include social networks, maps, and telephone networks.
This document summarizes the DBSCAN clustering algorithm. DBSCAN finds clusters based on density, requiring only two parameters: Eps, which defines the neighborhood distance, and MinPts, the minimum number of points required to form a cluster. It can discover clusters of arbitrary shape. The algorithm works by expanding clusters from core points, which have at least MinPts points within their Eps-neighborhood. Points that are not part of any cluster are classified as noise. Applications include spatial data analysis, image segmentation, and automatic border detection in medical images.
Ashish garg research paper 660_CamReadyAshish Garg
This document presents a hybrid sorting technique called CutShort that aims to optimize the runtime of sorting algorithms. It works by first dividing the input array into subarrays based on the number of bits needed to represent each element. The elements are then repositioned within the input array according to their subarray. Each subarray is then sorted independently using an optimal sorting algorithm like insertion sort. Experimental results on random, worst-case, and favorable data show that combining CutShort with quicksort, mergesort, or insertion sort reduces sorting time significantly compared to using the base algorithms alone. The technique is most effective when the input can be divided into many subarrays of more equal sizes.
The document discusses efficient codebook design for image compression using vector quantization. It introduces data compression techniques, including lossless compression methods like dictionary coders and entropy coding, as well as lossy compression methods like scalar and vector quantization. Vector quantization maps vectors to codewords in a codebook to compress data. The LBG algorithm is described for generating an optimal codebook by iteratively clustering vectors and updating codebook centroids.
The document describes an algorithm for automatically segmenting and tracking a speaker's lip contours from video. The algorithm first converts the video frames from RGB to HI (hue, intensity) color space. It then uses a statistical approach with Markov random fields to segment the mouth area, incorporating red hue and motion into a spatiotemporal neighborhood model. Simultaneously, it extracts a region of interest and relevant boundary points. Next, an active contour algorithm with spatially varying coefficients is initialized using the preprocessing results. This improves the active contours' performance by starting them close to the desired features. Finally, the algorithm accurately obtains the lip shape with inner and outer borders, achieving good quality results under challenging conditions.
The document discusses K-means clustering, an unsupervised machine learning algorithm that partitions observations into k clusters where each observation belongs to the cluster with the nearest mean. It describes how K-means aims to minimize intra-cluster similarity while maximizing inter-cluster similarity. The algorithm works by first selecting k random cluster centroids, then iteratively reassigning observations to the closest centroid and recalculating the centroids until convergence is reached. It also addresses computational complexity, extensions, tools for implementing K-means, and examples of applications like image compression, recommendation systems, and yield management.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmc
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In
this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected
weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the
number of processors by fraction 1/f (n) and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an
arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on
EREWPRAM model. In general, the proposed algorithm is the simplest one.
This document describes Dijkstra's algorithm, a greedy algorithm used to find the shortest paths between nodes in a graph. It explains that Dijkstra's algorithm works by assigning permanent labels to nodes starting with the source node, then iteratively assigning temporary labels to neighboring nodes to track the shortest path distances from the source. The algorithm is demonstrated on a sample graph with 6 nodes labeled A through T, showing how it progressively assigns labels to nodes in order to find the shortest path from node S to node T.
The document discusses graph-based clustering methods. It describes how graphs can be used to represent real-world networks from domains like biology, technology, social networks, and economics. It introduces the idea of using minimal spanning trees and hierarchical clustering to identify clusters in graph data. Two common algorithms for finding minimal spanning trees are described: Prim's algorithm and Kruskal's algorithm. Different strategies for iteratively deleting branches from the minimal spanning tree are also summarized to form clusters, such as deleting the branch with the maximum weight or inconsistent branches based on a reference value.
Low Power Adaptive FIR Filter Based on Distributed ArithmeticIJERA Editor
This paper aims at implementation of a low power adaptive FIR filter based on distributed arithmetic (DA) with
low power, high throughput, and low area. Least Mean Square (LMS) Algorithm is used to update the weight
and decrease the mean square error between the current filter output and the desired response. The pipelined
Distributed Arithmetic table reduces switching activity and hence it reduces power. The power consumption is
reduced by keeping bit-clock used in carry-save accumulation much faster than clock of rest of the operations.
We have implemented it in Quartus II and found that there is a reduction in the total power and the core dynamic
power by 31.31% and 100.24% respectively when compared with the architecture without DA table
Dijkstra's algorithm is used to find the shortest path between nodes in a weighted graph. It works by assigning initial distances to all nodes from the starting node and updating them as shorter paths are found, extracting the node with the lowest distance, and updating distances for neighboring unvisited nodes. The algorithm returns the shortest distance and path between the starting node and all other nodes in the graph.
This paper proposes a method to jointly match multiple 3D meshes by maximizing pairwise feature affinities and cycle consistency across models. It formulates the matching problem as a low-rank matrix recovery problem and uses nuclear norm relaxation for rank minimization. An alternating minimization algorithm is used to efficiently solve the optimization problem. Experimental results show the method provides an order of magnitude speed-up compared to state-of-the-art algorithms based on semi-definite programming, while achieving competitive performance. It also introduces a distortion term to the pairwise matching to help match reflexive sub-parts of models distinctly.
Joint3DShapeMatching - a fast approach to 3D model matching using MatchALS 3...Mamoon Ismail Khalid
we extend the global optimization-based
approach of jointly matching a set of images to jointly
matching a set of 3D meshes. The estimated correspon
dences simultaneously maximize pairwise feature affini
ties and cycle consistency across multiple models. We
show that the low-rank matrix recovery problem can be
efficiently applied to the 3D meshes as well. The fast
alternating minimization algorithm helps to handle real
world practical problems with thousands of features. Ex
perimental results show that, unlike the state-of-the-art
algorithm which rely on semi-definite programming, our
algorithm provides an order of magnitude speed-up along
with competitive performance. Along with the joint shape
matching we propose an approach to apply a distortion
term in pairwise matching, which helps in successfully
matching the reflexive sub-parts of two models distinc
tively. In the end, we demonstrate the applicability of
the algorithm to match a set of 3D meshes of the SCAPE
benchmark database
This document describes a quadratic assignment problem (QAP) involving assigning 358 constraints and 50 variables. It provides an example of a QAP with 3 facilities and 3 locations. The QAP aims to assign facilities to locations in a way that minimizes total cost, which is a function of the flow between facilities and the distance between locations. Several applications of QAP are discussed, including facility location, scheduling, and ergonomic design problems.
The document discusses different clustering algorithms, including k-means and EM clustering. K-means aims to partition items into k clusters such that each item belongs to the cluster with the nearest mean. It works iteratively to assign items to centroids and recompute centroids until the clusters no longer change. EM clustering generalizes k-means by computing probabilities of cluster membership based on probability distributions, with the goal of maximizing the overall probability of items given the clusters. Both algorithms are used to group similar items in applications like market segmentation.
Linear regression [Theory and Application (In physics point of view) using py...ANIRBANMAJUMDAR18
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.
Dijkstra's algorithm is a solution to the single-source shortest path problem in graph theory. It finds the shortest paths from a source vertex to all other vertices in a weighted graph where all edge weights are non-negative. The algorithm uses a greedy approach, maintaining a set of vertices whose final shortest path from the source vertex has already been determined.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
Optics ordering points to identify the clustering structureRajesh Piryani
The presentation summarized the OPTICS (Ordering Points To Identify the Clustering Structure) algorithm, a density-based clustering algorithm that addresses some limitations of DBSCAN. OPTICS does not produce an explicit clustering but instead outputs an ordering of all objects based on their reachability distances, representing the intrinsic clustering structure. It works by iteratively expanding clusters and updating an ordering seeds list to generate the output ordering without requiring pre-specification of parameters like DBSCAN. The ordering can then be used to extract clusters for a range of density parameter values. An example applying OPTICS on a 2D dataset was provided to illustrate the algorithm.
The document discusses clustering techniques and provides details about the k-means clustering algorithm. It begins with an introduction to clustering and lists different clustering techniques. It then describes the k-means algorithm in detail, including how it works, the steps involved, and provides an example illustration. Finally, it discusses comments on the k-means algorithm, focusing on aspects like choosing the value of k, initializing cluster centroids, and different distance measurement methods.
This document provides an overview of representing graphs and Dijkstra's algorithm in Prolog. It discusses different ways to represent graphs in Prolog, including using edge clauses, a graph term, and an adjacency list. It then explains Dijkstra's algorithm for finding the shortest path between nodes in a graph and provides pseudocode for implementing it in Prolog using rules for operations like finding the minimum value and merging lists.
Dijkstra's algorithm finds the shortest path from a starting node to all other nodes in a graph. It does this by examining all possible paths from the starting node and progressively eliminating longer paths, until arriving at the shortest path to each node. Flooding is a simple routing algorithm where every incoming packet is sent through every outgoing link except the one it arrived on, ensuring delivery but wasting bandwidth through duplicate packets circulating forever without precautions.
Dijkstra's algorithm allows finding the shortest path between any two vertices in a graph. It works by overestimating the distance of each vertex from the starting point and then visiting neighbors to find shorter paths. The algorithm uses a greedy approach, finding the next best solution at each step. It maintains path distances in an array and maps each vertex to its predecessor in the shortest path. A priority queue is used to efficiently retrieve the closest vertex. The time complexity is O(E Log V) and space is O(V). Applications include social networks, maps, and telephone networks.
This document summarizes the DBSCAN clustering algorithm. DBSCAN finds clusters based on density, requiring only two parameters: Eps, which defines the neighborhood distance, and MinPts, the minimum number of points required to form a cluster. It can discover clusters of arbitrary shape. The algorithm works by expanding clusters from core points, which have at least MinPts points within their Eps-neighborhood. Points that are not part of any cluster are classified as noise. Applications include spatial data analysis, image segmentation, and automatic border detection in medical images.
Ashish garg research paper 660_CamReadyAshish Garg
This document presents a hybrid sorting technique called CutShort that aims to optimize the runtime of sorting algorithms. It works by first dividing the input array into subarrays based on the number of bits needed to represent each element. The elements are then repositioned within the input array according to their subarray. Each subarray is then sorted independently using an optimal sorting algorithm like insertion sort. Experimental results on random, worst-case, and favorable data show that combining CutShort with quicksort, mergesort, or insertion sort reduces sorting time significantly compared to using the base algorithms alone. The technique is most effective when the input can be divided into many subarrays of more equal sizes.
The document discusses efficient codebook design for image compression using vector quantization. It introduces data compression techniques, including lossless compression methods like dictionary coders and entropy coding, as well as lossy compression methods like scalar and vector quantization. Vector quantization maps vectors to codewords in a codebook to compress data. The LBG algorithm is described for generating an optimal codebook by iteratively clustering vectors and updating codebook centroids.
The document describes an algorithm for automatically segmenting and tracking a speaker's lip contours from video. The algorithm first converts the video frames from RGB to HI (hue, intensity) color space. It then uses a statistical approach with Markov random fields to segment the mouth area, incorporating red hue and motion into a spatiotemporal neighborhood model. Simultaneously, it extracts a region of interest and relevant boundary points. Next, an active contour algorithm with spatially varying coefficients is initialized using the preprocessing results. This improves the active contours' performance by starting them close to the desired features. Finally, the algorithm accurately obtains the lip shape with inner and outer borders, achieving good quality results under challenging conditions.
The document discusses K-means clustering, an unsupervised machine learning algorithm that partitions observations into k clusters where each observation belongs to the cluster with the nearest mean. It describes how K-means aims to minimize intra-cluster similarity while maximizing inter-cluster similarity. The algorithm works by first selecting k random cluster centroids, then iteratively reassigning observations to the closest centroid and recalculating the centroids until convergence is reached. It also addresses computational complexity, extensions, tools for implementing K-means, and examples of applications like image compression, recommendation systems, and yield management.
A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREEijscmc
Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In
this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected
weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the
number of processors by fraction 1/f (n) and the parallel work by the fraction O ( 1 lo g ( f ( n )) ),where f (n) is an
arbitrary function. In the case f (n) =1, the algorithm runs in logarithmic-time and use super linear work on
EREWPRAM model. In general, the proposed algorithm is the simplest one.
This document describes Dijkstra's algorithm, a greedy algorithm used to find the shortest paths between nodes in a graph. It explains that Dijkstra's algorithm works by assigning permanent labels to nodes starting with the source node, then iteratively assigning temporary labels to neighboring nodes to track the shortest path distances from the source. The algorithm is demonstrated on a sample graph with 6 nodes labeled A through T, showing how it progressively assigns labels to nodes in order to find the shortest path from node S to node T.
The document discusses graph-based clustering methods. It describes how graphs can be used to represent real-world networks from domains like biology, technology, social networks, and economics. It introduces the idea of using minimal spanning trees and hierarchical clustering to identify clusters in graph data. Two common algorithms for finding minimal spanning trees are described: Prim's algorithm and Kruskal's algorithm. Different strategies for iteratively deleting branches from the minimal spanning tree are also summarized to form clusters, such as deleting the branch with the maximum weight or inconsistent branches based on a reference value.
Low Power Adaptive FIR Filter Based on Distributed ArithmeticIJERA Editor
This paper aims at implementation of a low power adaptive FIR filter based on distributed arithmetic (DA) with
low power, high throughput, and low area. Least Mean Square (LMS) Algorithm is used to update the weight
and decrease the mean square error between the current filter output and the desired response. The pipelined
Distributed Arithmetic table reduces switching activity and hence it reduces power. The power consumption is
reduced by keeping bit-clock used in carry-save accumulation much faster than clock of rest of the operations.
We have implemented it in Quartus II and found that there is a reduction in the total power and the core dynamic
power by 31.31% and 100.24% respectively when compared with the architecture without DA table
Dijkstra's algorithm is used to find the shortest path between nodes in a weighted graph. It works by assigning initial distances to all nodes from the starting node and updating them as shorter paths are found, extracting the node with the lowest distance, and updating distances for neighboring unvisited nodes. The algorithm returns the shortest distance and path between the starting node and all other nodes in the graph.
This paper proposes a method to jointly match multiple 3D meshes by maximizing pairwise feature affinities and cycle consistency across models. It formulates the matching problem as a low-rank matrix recovery problem and uses nuclear norm relaxation for rank minimization. An alternating minimization algorithm is used to efficiently solve the optimization problem. Experimental results show the method provides an order of magnitude speed-up compared to state-of-the-art algorithms based on semi-definite programming, while achieving competitive performance. It also introduces a distortion term to the pairwise matching to help match reflexive sub-parts of models distinctly.
Joint3DShapeMatching - a fast approach to 3D model matching using MatchALS 3...Mamoon Ismail Khalid
we extend the global optimization-based
approach of jointly matching a set of images to jointly
matching a set of 3D meshes. The estimated correspon
dences simultaneously maximize pairwise feature affini
ties and cycle consistency across multiple models. We
show that the low-rank matrix recovery problem can be
efficiently applied to the 3D meshes as well. The fast
alternating minimization algorithm helps to handle real
world practical problems with thousands of features. Ex
perimental results show that, unlike the state-of-the-art
algorithm which rely on semi-definite programming, our
algorithm provides an order of magnitude speed-up along
with competitive performance. Along with the joint shape
matching we propose an approach to apply a distortion
term in pairwise matching, which helps in successfully
matching the reflexive sub-parts of two models distinc
tively. In the end, we demonstrate the applicability of
the algorithm to match a set of 3D meshes of the SCAPE
benchmark database
Performance Improvement of Vector Quantization with Bit-parallelism HardwareCSCJournals
Vector quantization is an elementary technique for image compression; however, searching for the nearest codeword in a codebook is time-consuming. In this work, we propose a hardware-based scheme by adopting bit-parallelism to prune unnecessary codewords. The new scheme uses a “Bit-mapped Look-up Table” to represent the positional information of the codewords. The lookup procedure can simply refer to the bitmaps to find the candidate codewords. Our simulation results further confirm the effectiveness of the proposed scheme.
The document discusses several topics:
1. It explains the stream data model architecture with a diagram showing streams entering a processing system and being stored in an archival store or working store.
2. It defines a Bloom filter and describes how to calculate the probability of a false positive.
3. It outlines the Girvan-Newman algorithm for detecting communities in a graph by calculating betweenness values and removing edges.
4. It mentions PageRank and the Flajolet-Martin algorithm for approximating the number of unique objects in a data stream.
Bag of Pursuits and Neural Gas for Improved Sparse CodinKarlos Svoboda
This document proposes a new method called Bag of Pursuits and Neural Gas for learning overcomplete dictionaries from sparse data representations. It improves upon existing methods like MOD and K-SVD by employing a "bag of pursuits" approach that considers multiple sparse coding approximations for each data point, rather than just the optimal one. This allows the use of a generalized Neural Gas algorithm to learn the dictionary in a soft-competitive manner, leading to better performance even with less sparse representations. The bag of pursuits extends orthogonal matching pursuit to retrieve not just the single best sparse code but an approximate set of the top sparse codes for each point.
This document outlines a method for constructing local clusters of a massive distributed graph in parallel. It does this through four main steps: (1) randomly selecting source vertices and cluster sizes, (2) computing approximate personal PageRank vectors in parallel using Pregel, (3) performing a sweep using MapReduce to produce local clusters, and (4) reconciling any cluster overlaps by assigning vertices to the lowest conductance cluster. The key contributions are algorithms for parallel approximate PageRank computation and MapReduce-based sweeping to find local clusters efficiently in distributed graphs. Experimental results demonstrate the quality of clusterings produced and the algorithm's scalability.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
1) The document proposes a new robust estimator called INAPSAC (Improved N Adjacent Points Sample Consensus) for image analysis tasks like corner detection.
2) An experiment applies INAPSAC, RANSAC, and NAPSAC to corner detection on different image types and compares processing times and number of corners detected.
3) The results show that INAPSAC has faster processing times and detects more corners than RANSAC and NAPSAC, demonstrating that it is more accurate for corner detection than existing methods.
This document summarizes an investigation of using a dual tree algorithm and space partitioning trees to approximate matrix multiplication more efficiently than the naive O(MDN) approach under certain conditions. It presents an algorithm that organizes the row vectors of the left matrix and column vectors of the right matrix into ball trees, then performs a dual tree comparison to estimate the product matrix entries. For this to provide better complexity than naive multiplication, the vectors must fall into clusters proportional to D^τ for some τ > 0. However, uniformly distributed vectors would result in exponentially small expected cluster sizes, limiting the practical applicability of this approach. Future work is needed to address this issue.
SUBGRAPH MATCHING WITH SET SIMILARITY IN A LARGE GRAPH DATABASE - IEEE PROJE...Nexgen Technology
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Report on Efficient Estimation for High Similarities using Odd Sketches
1. Efficient Estimation for High Similarities
using Odd Sketches
Michael Mitzenmacher Rasmus Pagh Ninh Pham
Harvard University IT University of Copenhagen IT University of Copenhagen
Reported by
Souop Fotso Jocelyn Axel
Softskills Seminar, January 2018
Abstract
This paper present the implementation and the evaluation of Odd Sketch,
a compact binary sketch for estimating the Jaccard similarity of two sets.
This method provide a highly space-efficient and time-efficient estimator for
sets of high similarity, which is relevant in applications such as web duplicate
detection, collaborative filtering, and association rule learning. The method
extends to weighted Jaccard similarity. Experimental results show that the
Odd Sketche is more efficient than b-bit minwise hashing schemes on associ-
ation rule learning and web duplicate detection tasks.
1. Introduction
The estimation of the Jaccard similarity is a fondamental problem in
many computer applications in which we deal with collections of sets con-
taining thousands (sometimes even billions) of items.
Given two sets S1 and S1 ( S1, S2 ⊆ Ω={0, 1, ..., D − 1} ) their similarity
can be quantified using the Jaccard similarity coeffcient:
J(S1, S2) =
|S1 ∩ S2|
|S1 ∪ S2|
The main challenge in many computer applications is to have an quick esti-
mate of J. Existing solutions while highly efficient in general, are not optimal
1
2. when J is close to 1. The paper present a novel solution, the Odd Sketch,
that yields improved precision in the high similarity regime.
2. Previous works
2.1. Minwise Hashing
Minwise hashing is a powerful algorithmic technique to estimate set sim-
ilarities, originally proposed by Broder et al. [1].
Given a random permutation π : Ω → Ω, the Jaccard similarity of S1 and S2 is
J(S1, S2) = Pr[min(π(S1)) = min(π(S2))]
where min(π (S1)) denotes the minhash of S1. Therefore we get an esti-
mator for J by considering a sequence of permutations π1,...,πk and storing
the annotated minhashes.
S1 = (i, min(πi(S1))) | i = 1, . . . , k ,
S1 = (i, min(πi(S2))) | i = 1, . . . , k .
We estimate J by the fraction:
ˆJ =
|S1 ∩ S2|
k
This estimator is unbiased, and by independence of the permutations it
can be shown that
V ar(ˆJ) =
J(J − 1)
k
2.2. b-bit Minwise Hashing
Li and Konig [2] proposed a time and space efficient version of the original
minwise hashing scheme. Instead of storing b = 32 or b = 64 bits for each
minhashes, this approach suggested using the lowest b bits. It is based on
the intuition that the same hash values give the same lowest b bits whereas
the different hash values give different lowest b bits with probability 1-1/2b
.
2
3. Proceeding similarly as done for the minhash but saving only the lowest b
bit for each set, we can have an estimate of J and its variance:
However for similarity close to 1, b-bit minhash will produce almost identical
sketches, which reveal very little about *how* close to 1 the similarity is.
Therefore this approach is non optimal in a high similarity regime.
3. Proposed solution
The authors proposed the Odd Sketch, a compact binary sketch similar
to a Bloom filter with one hash function, constructed on the original min-
hashes with the ”odd” feature that the usual disjunction is replaced by an
exclusive-or operation.
Given a set S, the odd sketch of set S that we denote by odd(S) is a binary
array of size n (n>2) that records in the ith position the parity of the number
of elements of set S that are hashed (by a fully random hash function) in
position i.
Here is a pseudo code of the Odd sketch construction:
Algorithm 1 Odd sketch (S,n)
Require: The set S and the size of sketch in bits n
1: Initialize the array A of size n to zero
2: Pick a random hash function h: Ω →[n]
3: for each set element x S do
4: A[h(x)]=A[h(x)] 1 //flip the bit in the ith=h(x) position
5: end for
6: return A
Because odd(S) records the parity of the number of elements that hash
to a location, it follows that :
3
4. The authors proved that if we construct the the Odd sketches Odd(S1) and
Odd(S2) from the Minhashes S1 and S2 derived from the original sets S1
and S2 we can estimate the Jaccard similarity coeffcient J( S1, S2) as follow:
Where k is the numbrer of permutation used during the minhash step.
Both Odd Sketches and b-bit minwise hashing can be viewed as variations of
the original minwise hashing scheme that reduce the number of bits used. The
quality of their estimators is dependent on the quality of the original minwise
estimators. In practice, both Odd Sketches and b-bit minwise hashing need
to use more permutations but less storage space than the original minwise
hashing scheme.
4. Evaluation Highlights
In oder to evaluate the performances, the authors implemented b-bit min-
wise hashing and odd sketch in matlab and compared the performances of
both approaches on Association rule learning and web duplication detection
tasks. It emerges that:
• Comparing the accuracy (-log(MSE)) of both approaches on a sparse
data set we note that Odd Sketch provides a smaller error than the
b-bit minwise approach even when both the approaches use the same
number of permutation. The difference is more dramatic when J is very
high
• Association rule learning: The authors measured the precision-
recall ratio of both approaches on detecting the pairwise items that
have Jaccard similarity larger than a threshold J0 =0.9 . The results
obtained demonstrate the superiority of Odd Sketch compared to 1/2-
bit minwise hashing with respect to precision. The Odd Sketch achieved
up to 20% higher precision while providing similar recall.
4
5. • Web duplicate detection:
In this experiment, the authors compared the performance of the two
approaches on web duplicate detection tasks on the bag of words dataset
. They picked three high dimensional datasets and computed all pair-
wise Jaccard similarities among documents, and retrieved every pair
with J ≥ J0. For the sake of comparison, they used the same number
of permutations and considered the thresholds J0 = 0.85 and J0 = 0.90.
The precision-recall ratio were used again as the standard measure. It
comes out that Odd Sketch is still better in precision but slightly worse
in recall.
5. CONCLUSION
The paper presented the Odd Sketch, a compact binary sketch for esti-
mating similarity of two sets. Odd Sketch is time and space efficient and gives
good results even in the high similarity regime. Experiments on synthetic
and real world datasets demonstrate the efficiency of Odd Sketches in com-
parison with b-bit minwise hashing schemes on association rule learning and
web duplicate detection tasks. From the authors, there is great expectation
that the odd sketch will bee used for other applications.
6. RFERENCES
[1] A. Z. Broder, M. Charikar, A. M. Frieze, and M. Mitzenmacher. Min-wise
independent permutations. J. Comput. Syst. Sci., 60(3):630659, 2000.
[2] P. Li and A. C. K¨onig. b-bit minwise hashing. In WWW, pages 671680,
2010
5