# A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks

Save this PDF as:

Size: px
Start display at page:

Download "A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks"

## Transcription

3 (a) 3 targets with 3 antenna orientations Fig. 1: Sensors and targets in the same region. (b) 19 sensors with 19 antenna orientations We now consider the principal and second eigenvector of A T A, as shown in Figures 4 and 5, respectively. At first glance, it may be difficult to see immediately how these two eigenvectors relate to polarization matching between sensors and targets. This will become clear when we look at the bipartite sensor-target graph of Figure 6, where the colored edges represent scores of Figure 2. That is, colorcoded scores are blue = 1, green = 0.5 and red = 0.1. First, let s look at the principal eigenvector of Figure 4. A common way to interpret its components is that they represent the stationary probabilities that a random traversal of the graph of Figure 6 will land at any given sensor node. Indeed, one can show (e.g., by the Perron- Frobenius theorem [7]) that all the components of the principal eigenvector are all positive (or equivalently, all negative) as in Figure 4. The values of these components, which correspond to sensor nodes, reflect connectivity as well as edge weights of the graph. However, there could be aliases in the sense that multiple clusters may attain the same component value in the first principal eigenvector. For example, in Figure 4, sensors 4, 5, 13 and 14 all have value.05, and thus the eigenvector implies that {4, 5, 13, 14} is a cluster. However, in Figure 6 we see that sensors 4 and 5 should form a cluster separated from that of sensors 13 and 14, since the former has a connection to target 0 while the latter has a connection to target 2. Similarly, the first principal eigenvector of Figure 4 mistakenly identifies clusters {2, 3, 15, 16} and {0, 1, 17, 18}. Next, we look at the second eigenvector of Figure 5. Fig. 4: The principal eigenvector of A T A, with values of its elements (also called components) shown. Note that components here correspond to sensor nodes. It has seven distinct values. These imply seven clusters: {0, 1}, {2, 3}, {4, 5}, {6, 7, 8, 9, 10, 11, 12}, {13, 14}, {15, 16}, and {17, 18}. One can check that the second eigenvector has now fixed all the mistaken clusters identified by the first eigenvector, except for mistakenly identifying {6, 7, 8, 9, 10, 11, 12} as a cluster due to aliasing. We see from Figure 6 that although all these seven nodes connect to target 1, sensors 8, 9 and 10 connect to target 1 with blue connections, while sensors 6, 7, 11 and 12 with green connections. Thus {8, 9, 10} and {6, 7, 11, 12} should form two clusters. One can check that this

4 partition of {6, 7, 8, 9, 10, 11, 12} into these two clusters is actually implied by the principal eigenvector of Figure 4, as the two groups attain two distinct values 0.25 and.5. Thus, for this example, by using both the first and second eigenvectors together, we have obtained the correct eight clusters: {0, 1}, {2, 3}, {4, 5}, {8, 9, 10}, {6, 7, 11, 12}, {13, 14}, {15, 16}, and {17, 18}. Fig. 5: The second eigenvector of A T A with values of its elements (also called components) shown. Note that components here correspond to sensor nodes. Fig. 6: Bipartite sensor-target score graph, where colorcoded scores are blue = 1, green = 0.5 and red = 0.1. The seven sensor clusters shown are those found by the second eigenvector of Figure 5. Note that with the help of the principal eigenvector of Figure 4, cluster 4 will be correctly partitioned into the two clusters {8, 9, 10} and {6, 7, 11, 12}. We have seen in this example that the principal and second eigenvectors complement each other, in the sense that each can fix the alias problems of the other. This phenomenon is not an accident. Without loss of generality, we consider the case that eigenvectors are computed by the power method. Note that because the matrix A has non-negative entries, using a positive initial vector for the power method results in the principal eigenvector having aliased values when the underlying graph is a symmetric bipartite graph, as in Figure 6. Being orthogonal to the principal eigenvector, the second one must contain both positive and negative components, and as a result, it does not exhibit the same alias problems as the first one. But due to cancellation resulting from combining positive and negative values, the second eigenvector may suffer from other alias problems, which the first one does not share since all its values are positive. This means that the principal and second eigenvectors can fix each other s aliases. (We note that the use of leading eigenvectors in this manner is a technique also known to multidimensional scaling, a statistical method for computing data similarity. [8]) Using this joint approach of principal and non-principal eigenvectors, we have a general method of automatically finding sensor clusters which match individual targets. IV. SIGN-BASED SPECTRAL CLUSTERING From our arguments in the preceding section, we consider here a sign-based spectral clustering. Suppose that we use the leading k eigenvectors. Multiple sensors will be clustered together only if their corresponding components in these k eigenvectors have matching signs. (Note that k eigenvectors can specify no more than 2 k 1 clusters, given that the principal eigenvector always contains non-negative components.) As an example, this sign-based process of clustering of the sensors in Figure 6 with k = 3 is shown in Figure 7. Note that for the same matrix A in Figure 3, sign-based clustering gives three clusters using three leading eigenvectors, while the value-based clustering described in the preceding section gives seven clusters. It is expected that the sign-based clustering generally gives coarse clustering, since only signs of component values rather than their actual values are used. In practice, sign-based clustering is robust against those sensor measurements which may have significant variation. In this case, component values of eigenvectors will have enough variance so their precise values can not be used. Sign-based clustering is a method to address this uncertainty in sensor measurements. V. SENSOR VALIDATION: ILLUSTRATIVE EXAMPLE OF DETECTING BAD SENSORS AND DESIGN CONSIDERATIONS In this section, we first illustrate how our spectral clustering method can identify a bad sensor for the model problem described in Section III. We then describe some considerations in designing a spectral clustering scheme for detecting bad sensors.

### DATA ANALYSIS II. Matrix Algorithms

DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where

### UNCOUPLING THE PERRON EIGENVECTOR PROBLEM

UNCOUPLING THE PERRON EIGENVECTOR PROBLEM Carl D Meyer INTRODUCTION Foranonnegative irreducible matrix m m with spectral radius ρ,afundamental problem concerns the determination of the unique normalized

### A Direct Numerical Method for Observability Analysis

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL 15, NO 2, MAY 2000 625 A Direct Numerical Method for Observability Analysis Bei Gou and Ali Abur, Senior Member, IEEE Abstract This paper presents an algebraic method

### USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE- FREE NETWORKS AND SMALL-WORLD NETWORKS

USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE- FREE NETWORKS AND SMALL-WORLD NETWORKS Natarajan Meghanathan Jackson State University, 1400 Lynch St, Jackson, MS, USA natarajan.meghanathan@jsums.edu

### Spectral graph theory

Spectral graph theory Uri Feige January 2010 1 Background With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian

### Mining Social-Network Graphs

342 Chapter 10 Mining Social-Network Graphs There is much information to be gained by analyzing the large-scale data that is derived from social networks. The best-known example of a social network is

### Methodology for Emulating Self Organizing Maps for Visualization of Large Datasets

Methodology for Emulating Self Organizing Maps for Visualization of Large Datasets Macario O. Cordel II and Arnulfo P. Azcarraga College of Computer Studies *Corresponding Author: macario.cordel@dlsu.edu.ph

### Face Recognition using Principle Component Analysis

Face Recognition using Principle Component Analysis Kyungnam Kim Department of Computer Science University of Maryland, College Park MD 20742, USA Summary This is the summary of the basic idea about PCA

### Component Ordering in Independent Component Analysis Based on Data Power

Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, Signals

### OPTIMAL DESIGN OF DISTRIBUTED SENSOR NETWORKS FOR FIELD RECONSTRUCTION

OPTIMAL DESIGN OF DISTRIBUTED SENSOR NETWORKS FOR FIELD RECONSTRUCTION Sérgio Pequito, Stephen Kruzick, Soummya Kar, José M. F. Moura, A. Pedro Aguiar Department of Electrical and Computer Engineering

### NETZCOPE - a tool to analyze and display complex R&D collaboration networks

The Task Concepts from Spectral Graph Theory EU R&D Network Analysis Netzcope Screenshots NETZCOPE - a tool to analyze and display complex R&D collaboration networks L. Streit & O. Strogan BiBoS, Univ.

### The Power Method for Eigenvalues and Eigenvectors

Numerical Analysis Massoud Malek The Power Method for Eigenvalues and Eigenvectors The spectrum of a square matrix A, denoted by σ(a) is the set of all eigenvalues of A. The spectral radius of A, denoted

### USE OF EIGENVALUES AND EIGENVECTORS TO ANALYZE BIPARTIVITY OF NETWORK GRAPHS

USE OF EIGENVALUES AND EIGENVECTORS TO ANALYZE BIPARTIVITY OF NETWORK GRAPHS Natarajan Meghanathan Jackson State University, 1400 Lynch St, Jackson, MS, USA natarajan.meghanathan@jsums.edu ABSTRACT This

### Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm

1 Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm Hani Mehrpouyan, Student Member, IEEE, Department of Electrical and Computer Engineering Queen s University, Kingston, Ontario,

### NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES

NEW VERSION OF DECISION SUPPORT SYSTEM FOR EVALUATING TAKEOVER BIDS IN PRIVATIZATION OF THE PUBLIC ENTERPRISES AND SERVICES Silvija Vlah Kristina Soric Visnja Vojvodic Rosenzweig Department of Mathematics

### 1 Example of Time Series Analysis by SSA 1

1 Example of Time Series Analysis by SSA 1 Let us illustrate the 'Caterpillar'-SSA technique [1] by the example of time series analysis. Consider the time series FORT (monthly volumes of fortied wine sales

### Part 2: Community Detection

Chapter 8: Graph Data Part 2: Community Detection Based on Leskovec, Rajaraman, Ullman 2014: Mining of Massive Datasets Big Data Management and Analytics Outline Community Detection - Social networks -

### Expander Graph based Key Distribution Mechanisms in Wireless Sensor Networks

Expander Graph based Key Distribution Mechanisms in Wireless Sensor Networks Seyit Ahmet Çamtepe Computer Science Department Rensselaer Polytechnic Institute Troy, New York 12180 Email: camtes@cs.rpi.edu

### Practical Graph Mining with R. 5. Link Analysis

Practical Graph Mining with R 5. Link Analysis Outline Link Analysis Concepts Metrics for Analyzing Networks PageRank HITS Link Prediction 2 Link Analysis Concepts Link A relationship between two entities

### SpotFi: Decimeter Level Localization Using WiFi

SpotFi: Decimeter Level Localization Using WiFi Hasan Faik Alan Kotaru, Manikanta, Kiran Joshi, Dinesh Bharadia, and Sachin Katti. "SpotFi: Decimeter Level Localization Using WiFi." In Proceedings of the

### Comparison of Non-linear Dimensionality Reduction Techniques for Classification with Gene Expression Microarray Data

CMPE 59H Comparison of Non-linear Dimensionality Reduction Techniques for Classification with Gene Expression Microarray Data Term Project Report Fatma Güney, Kübra Kalkan 1/15/2013 Keywords: Non-linear

### 15.062 Data Mining: Algorithms and Applications Matrix Math Review

.6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop

### TAGUCHI APPROACH TO DESIGN OPTIMIZATION FOR QUALITY AND COST: AN OVERVIEW. Resit Unal. Edwin B. Dean

TAGUCHI APPROACH TO DESIGN OPTIMIZATION FOR QUALITY AND COST: AN OVERVIEW Resit Unal Edwin B. Dean INTRODUCTION Calibrations to existing cost of doing business in space indicate that to establish human

### APPM4720/5720: Fast algorithms for big data. Gunnar Martinsson The University of Colorado at Boulder

APPM4720/5720: Fast algorithms for big data Gunnar Martinsson The University of Colorado at Boulder Course objectives: The purpose of this course is to teach efficient algorithms for processing very large

### Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components

Eigenvalues, Eigenvectors, Matrix Factoring, and Principal Components The eigenvalues and eigenvectors of a square matrix play a key role in some important operations in statistics. In particular, they

### Circuits 1 M H Miller

Introduction to Graph Theory Introduction These notes are primarily a digression to provide general background remarks. The subject is an efficient procedure for the determination of voltages and currents

### S = {1, 2,..., n}. P (1, 1) P (1, 2)... P (1, n) P (2, 1) P (2, 2)... P (2, n) P = . P (n, 1) P (n, 2)... P (n, n)

last revised: 26 January 2009 1 Markov Chains A Markov chain process is a simple type of stochastic process with many social science applications. We ll start with an abstract description before moving

### A Comparison of General Approaches to Multiprocessor Scheduling

A Comparison of General Approaches to Multiprocessor Scheduling Jing-Chiou Liou AT&T Laboratories Middletown, NJ 0778, USA jing@jolt.mt.att.com Michael A. Palis Department of Computer Science Rutgers University

### 4.9 Markov matrices. DEFINITION 4.3 A real n n matrix A = [a ij ] is called a Markov matrix, or row stochastic matrix if. (i) a ij 0 for 1 i, j n;

49 Markov matrices DEFINITION 43 A real n n matrix A = [a ij ] is called a Markov matrix, or row stochastic matrix if (i) a ij 0 for 1 i, j n; (ii) a ij = 1 for 1 i n Remark: (ii) is equivalent to AJ n

### In the following we will only consider undirected networks.

Roles in Networks Roles in Networks Motivation for work: Let topology define network roles. Work by Kleinberg on directed graphs, used topology to define two types of roles: authorities and hubs. (Each

### IMPROVED NETWORK PARAMETER ERROR IDENTIFICATION USING MULTIPLE MEASUREMENT SCANS

IMPROVED NETWORK PARAMETER ERROR IDENTIFICATION USING MULTIPLE MEASUREMENT SCANS Liuxi Zhang and Ali Abur Department of Electrical and Computer Engineering Northeastern University Boston, MA, USA lzhang@ece.neu.edu

### EFFICIENT DETECTION IN DDOS ATTACK FOR TOPOLOGY GRAPH DEPENDENT PERFORMANCE IN PPM LARGE SCALE IPTRACEBACK

EFFICIENT DETECTION IN DDOS ATTACK FOR TOPOLOGY GRAPH DEPENDENT PERFORMANCE IN PPM LARGE SCALE IPTRACEBACK S.Abarna 1, R.Padmapriya 2 1 Mphil Scholar, 2 Assistant Professor, Department of Computer Science,

### Bindel, Fall 2012 Matrix Computations (CS 6210) Week 8: Friday, Oct 12

Why eigenvalues? Week 8: Friday, Oct 12 I spend a lot of time thinking about eigenvalue problems. In part, this is because I look for problems that can be solved via eigenvalues. But I might have fewer

### A Regime-Switching Model for Electricity Spot Prices. Gero Schindlmayr EnBW Trading GmbH g.schindlmayr@enbw.com

A Regime-Switching Model for Electricity Spot Prices Gero Schindlmayr EnBW Trading GmbH g.schindlmayr@enbw.com May 31, 25 A Regime-Switching Model for Electricity Spot Prices Abstract Electricity markets

### Key words. cluster analysis, k-means, eigen decomposition, Laplacian matrix, data visualization, Fisher s Iris data set

SPECTRAL CLUSTERING AND VISUALIZATION: A NOVEL CLUSTERING OF FISHER S IRIS DATA SET DAVID BENSON-PUTNINS, MARGARET BONFARDIN, MEAGAN E. MAGNONI, AND DANIEL MARTIN Advisors: Carl D. Meyer and Charles D.

### Notes for STA 437/1005 Methods for Multivariate Data

Notes for STA 437/1005 Methods for Multivariate Data Radford M. Neal, 26 November 2010 Random Vectors Notation: Let X be a random vector with p elements, so that X = [X 1,..., X p ], where denotes transpose.

### Data Clustering. Dec 2nd, 2013 Kyrylo Bessonov

Data Clustering Dec 2nd, 2013 Kyrylo Bessonov Talk outline Introduction to clustering Types of clustering Supervised Unsupervised Similarity measures Main clustering algorithms k-means Hierarchical Main

### Solution based on matrix technique Rewrite. ) = 8x 2 1 4x 1x 2 + 5x x1 2x 2 2x 1 + 5x 2

8.2 Quadratic Forms Example 1 Consider the function q(x 1, x 2 ) = 8x 2 1 4x 1x 2 + 5x 2 2 Determine whether q(0, 0) is the global minimum. Solution based on matrix technique Rewrite q( x1 x 2 = x1 ) =

### Motion Sensing without Sensors: Information. Harvesting from Signal Strength Measurements

Motion Sensing without Sensors: Information Harvesting from Signal Strength Measurements D. Puccinelli and M. Haenggi Department of Electrical Engineering University of Notre Dame Notre Dame, Indiana,

### A CHARACTERIZATION OF TREE TYPE

A CHARACTERIZATION OF TREE TYPE LON H MITCHELL Abstract Let L(G) be the Laplacian matrix of a simple graph G The characteristic valuation associated with the algebraic connectivity a(g) is used in classifying

### Social Media Mining. Network Measures

Klout Measures and Metrics 22 Why Do We Need Measures? Who are the central figures (influential individuals) in the network? What interaction patterns are common in friends? Who are the like-minded users

### ON THE DEGREES OF FREEDOM OF SIGNALS ON GRAPHS. Mikhail Tsitsvero and Sergio Barbarossa

ON THE DEGREES OF FREEDOM OF SIGNALS ON GRAPHS Mikhail Tsitsvero and Sergio Barbarossa Sapienza Univ. of Rome, DIET Dept., Via Eudossiana 18, 00184 Rome, Italy E-mail: tsitsvero@gmail.com, sergio.barbarossa@uniroma1.it

### IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 20, NO. 7, JULY 2009 1181 The Global Kernel k-means Algorithm for Clustering in Feature Space Grigorios F. Tzortzis and Aristidis C. Likas, Senior Member, IEEE

### Dynamic Load Balance Algorithm (DLBA) for IEEE 802.11 Wireless LAN

Tamkang Journal of Science and Engineering, vol. 2, No. 1 pp. 45-52 (1999) 45 Dynamic Load Balance Algorithm () for IEEE 802.11 Wireless LAN Shiann-Tsong Sheu and Chih-Chiang Wu Department of Electrical

### Dimensionality Reduction: Principal Components Analysis

Dimensionality Reduction: Principal Components Analysis In data mining one often encounters situations where there are a large number of variables in the database. In such situations it is very likely

### SYMMETRIC EIGENFACES MILI I. SHAH

SYMMETRIC EIGENFACES MILI I. SHAH Abstract. Over the years, mathematicians and computer scientists have produced an extensive body of work in the area of facial analysis. Several facial analysis algorithms

### Analysis of Internet Topologies: A Historical View

Analysis of Internet Topologies: A Historical View Mohamadreza Najiminaini, Laxmi Subedi, and Ljiljana Trajković Communication Networks Laboratory http://www.ensc.sfu.ca/cnl Simon Fraser University Vancouver,

### An Empirical Approach - Distributed Mobility Management for Target Tracking in MANETs

An Empirical Approach - Distributed Mobility Management for Target Tracking in MANETs G.Michael Assistant Professor, Department of CSE, Bharath University, Chennai, TN, India ABSTRACT: Mobility management

### Performance of Dynamic Load Balancing Algorithms for Unstructured Mesh Calculations

Performance of Dynamic Load Balancing Algorithms for Unstructured Mesh Calculations Roy D. Williams, 1990 Presented by Chris Eldred Outline Summary Finite Element Solver Load Balancing Results Types Conclusions

### COMPUTING CLOUD MOTION USING A CORRELATION RELAXATION ALGORITHM Improving Estimation by Exploiting Problem Knowledge Q. X. WU

COMPUTING CLOUD MOTION USING A CORRELATION RELAXATION ALGORITHM Improving Estimation by Exploiting Problem Knowledge Q. X. WU Image Processing Group, Landcare Research New Zealand P.O. Box 38491, Wellington

### Similarity and Diagonalization. Similar Matrices

MATH022 Linear Algebra Brief lecture notes 48 Similarity and Diagonalization Similar Matrices Let A and B be n n matrices. We say that A is similar to B if there is an invertible n n matrix P such that

### Walk-Based Centrality and Communicability Measures for Network Analysis

Walk-Based Centrality and Communicability Measures for Network Analysis Michele Benzi Department of Mathematics and Computer Science Emory University Atlanta, Georgia, USA Workshop on Innovative Clustering

### Calibrating a Camera and Rebuilding a Scene by Detecting a Fixed Size Common Object in an Image

Calibrating a Camera and Rebuilding a Scene by Detecting a Fixed Size Common Object in an Image Levi Franklin Section 1: Introduction One of the difficulties of trying to determine information about a

### Performance Metrics for Graph Mining Tasks

Performance Metrics for Graph Mining Tasks 1 Outline Introduction to Performance Metrics Supervised Learning Performance Metrics Unsupervised Learning Performance Metrics Optimizing Metrics Statistical

### 6.042/18.062J Mathematics for Computer Science October 3, 2006 Tom Leighton and Ronitt Rubinfeld. Graph Theory III

6.04/8.06J Mathematics for Computer Science October 3, 006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Graph Theory III Draft: please check back in a couple of days for a modified version of these

### A Network Flow Approach in Cloud Computing

1 A Network Flow Approach in Cloud Computing Soheil Feizi, Amy Zhang, Muriel Médard RLE at MIT Abstract In this paper, by using network flow principles, we propose algorithms to address various challenges

### α = u v. In other words, Orthogonal Projection

Orthogonal Projection Given any nonzero vector v, it is possible to decompose an arbitrary vector u into a component that points in the direction of v and one that points in a direction orthogonal to v

### ISSN: Mohammad Mofarreh Bonab et al, International Journal of Computer Science & Communication Networks,Vol 2(1),

A New Technique for Image Compression Using PCA Mohammad Mofarreh-Bonab 1, Mostafa Mofarreh-Bonab 2 1 University of Bonab, East Azerbaijan, Iran 2 Shahid Beheshti University, Tehran, Iran 1 mmofarreh@gmailcom

### THREE DIMENSIONAL REPRESENTATION OF AMINO ACID CHARAC- TERISTICS

THREE DIMENSIONAL REPRESENTATION OF AMINO ACID CHARAC- TERISTICS O.U. Sezerman 1, R. Islamaj 2, E. Alpaydin 2 1 Laborotory of Computational Biology, Sabancı University, Istanbul, Turkey. 2 Computer Engineering

### Performance of TD-CDMA systems during crossed slots

Performance of TD-CDMA systems during s Jad NASREDDINE and Xavier LAGRANGE Multimedia Networks and Services Department, GET / ENST de Bretagne 2 rue de la châtaigneraie, CS 1767, 35576 Cesson Sévigné Cedex,

### Markov Chains, part I

Markov Chains, part I December 8, 2010 1 Introduction A Markov Chain is a sequence of random variables X 0, X 1,, where each X i S, such that P(X i+1 = s i+1 X i = s i, X i 1 = s i 1,, X 0 = s 0 ) = P(X

### Analysis of Internet Topologies

Analysis of Internet Topologies Ljiljana Trajković ljilja@cs.sfu.ca Communication Networks Laboratory http://www.ensc.sfu.ca/cnl School of Engineering Science Simon Fraser University, Vancouver, British

### Markov chains and Markov Random Fields (MRFs)

Markov chains and Markov Random Fields (MRFs) 1 Why Markov Models We discuss Markov models now. This is the simplest statistical model in which we don t assume that all variables are independent; we assume

### ON THE COMPLEXITY OF THE GAME OF SET. {kamalika,pbg,dratajcz,hoeteck}@cs.berkeley.edu

ON THE COMPLEXITY OF THE GAME OF SET KAMALIKA CHAUDHURI, BRIGHTEN GODFREY, DAVID RATAJCZAK, AND HOETECK WEE {kamalika,pbg,dratajcz,hoeteck}@cs.berkeley.edu ABSTRACT. Set R is a card game played with a

### Chapter 6. Orthogonality

6.3 Orthogonal Matrices 1 Chapter 6. Orthogonality 6.3 Orthogonal Matrices Definition 6.4. An n n matrix A is orthogonal if A T A = I. Note. We will see that the columns of an orthogonal matrix must be

### Least-Squares Intersection of Lines

Least-Squares Intersection of Lines Johannes Traa - UIUC 2013 This write-up derives the least-squares solution for the intersection of lines. In the general case, a set of lines will not intersect at a

### Nonlinear Iterative Partial Least Squares Method

Numerical Methods for Determining Principal Component Analysis Abstract Factors Béchu, S., Richard-Plouet, M., Fernandez, V., Walton, J., and Fairley, N. (2016) Developments in numerical treatments for

### Notes on Symmetric Matrices

CPSC 536N: Randomized Algorithms 2011-12 Term 2 Notes on Symmetric Matrices Prof. Nick Harvey University of British Columbia 1 Symmetric Matrices We review some basic results concerning symmetric matrices.

### Mini-project in TSRT04: Cell Phone Coverage

Mini-project in TSRT04: Cell hone Coverage 19 August 2015 1 roblem Formulation According to the study Swedes and Internet 2013 (Stiftelsen för Internetinfrastruktur), 99% of all Swedes in the age 12-45

### Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs

CSE599s: Extremal Combinatorics November 21, 2011 Lecture 15 An Arithmetic Circuit Lowerbound and Flows in Graphs Lecturer: Anup Rao 1 An Arithmetic Circuit Lower Bound An arithmetic circuit is just like

### The Second Eigenvalue of the Google Matrix

0 2 The Second Eigenvalue of the Google Matrix Taher H Haveliwala and Sepandar D Kamvar Stanford University taherh,sdkamvar @csstanfordedu Abstract We determine analytically the modulus of the second eigenvalue

### MUSIC-like Processing of Pulsed Continuous Wave Signals in Active Sonar Experiments

23rd European Signal Processing Conference EUSIPCO) MUSIC-like Processing of Pulsed Continuous Wave Signals in Active Sonar Experiments Hock Siong LIM hales Research and echnology, Singapore hales Solutions

### Review Jeopardy. Blue vs. Orange. Review Jeopardy

Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 0-3 Jeopardy Round \$200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?

### An Improved Spectral Load Balancing Method*

SAND93-016C An Improved Spectral Load Balancing Method* Bruce Hendrickson Robert Leland Abstract We describe an algorithm for the static load balancing of scientific computations that generalizes and improves

### Performance of networks containing both MaxNet and SumNet links

Performance of networks containing both MaxNet and SumNet links Lachlan L. H. Andrew and Bartek P. Wydrowski Abstract Both MaxNet and SumNet are distributed congestion control architectures suitable for

### Performance Analysis of Naive Bayes and J48 Classification Algorithm for Data Classification

Performance Analysis of Naive Bayes and J48 Classification Algorithm for Data Classification Tina R. Patil, Mrs. S. S. Sherekar Sant Gadgebaba Amravati University, Amravati tnpatil2@gmail.com, ss_sherekar@rediffmail.com

### Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

### Approximated Distributed Minimum Vertex Cover Algorithms for Bounded Degree Graphs

Approximated Distributed Minimum Vertex Cover Algorithms for Bounded Degree Graphs Yong Zhang 1.2, Francis Y.L. Chin 2, and Hing-Fung Ting 2 1 College of Mathematics and Computer Science, Hebei University,

### Lecture 9. 1 Introduction. 2 Random Walks in Graphs. 1.1 How To Explore a Graph? CS-621 Theory Gems October 17, 2012

CS-62 Theory Gems October 7, 202 Lecture 9 Lecturer: Aleksander Mądry Scribes: Dorina Thanou, Xiaowen Dong Introduction Over the next couple of lectures, our focus will be on graphs. Graphs are one of

### A Piggybacking Design Framework for Read-and Download-efficient Distributed Storage Codes

A Piggybacing Design Framewor for Read-and Download-efficient Distributed Storage Codes K V Rashmi, Nihar B Shah, Kannan Ramchandran, Fellow, IEEE Department of Electrical Engineering and Computer Sciences

### 0.1 Phase Estimation Technique

Phase Estimation In this lecture we will describe Kitaev s phase estimation algorithm, and use it to obtain an alternate derivation of a quantum factoring algorithm We will also use this technique to design

### BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES

BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES 123 CHAPTER 7 BEHAVIOR BASED CREDIT CARD FRAUD DETECTION USING SUPPORT VECTOR MACHINES 7.1 Introduction Even though using SVM presents

### Subspace Analysis and Optimization for AAM Based Face Alignment

Subspace Analysis and Optimization for AAM Based Face Alignment Ming Zhao Chun Chen College of Computer Science Zhejiang University Hangzhou, 310027, P.R.China zhaoming1999@zju.edu.cn Stan Z. Li Microsoft

### Prediction of DDoS Attack Scheme

Chapter 5 Prediction of DDoS Attack Scheme Distributed denial of service attack can be launched by malicious nodes participating in the attack, exploit the lack of entry point in a wireless network, and

### Chapter 15 Introduction to Linear Programming

Chapter 15 Introduction to Linear Programming An Introduction to Optimization Spring, 2014 Wei-Ta Chu 1 Brief History of Linear Programming The goal of linear programming is to determine the values of

### Decision-making with the AHP: Why is the principal eigenvector necessary

European Journal of Operational Research 145 (2003) 85 91 Decision Aiding Decision-making with the AHP: Why is the principal eigenvector necessary Thomas L. Saaty * University of Pittsburgh, Pittsburgh,

### (67902) Topics in Theory and Complexity Nov 2, 2006. Lecture 7

(67902) Topics in Theory and Complexity Nov 2, 2006 Lecturer: Irit Dinur Lecture 7 Scribe: Rani Lekach 1 Lecture overview This Lecture consists of two parts In the first part we will refresh the definition

### Computational Optical Imaging - Optique Numerique. -- Deconvolution --

Computational Optical Imaging - Optique Numerique -- Deconvolution -- Winter 2014 Ivo Ihrke Deconvolution Ivo Ihrke Outline Deconvolution Theory example 1D deconvolution Fourier method Algebraic method

### IJCSES Vol.7 No.4 October 2013 pp.165-168 Serials Publications BEHAVIOR PERDITION VIA MINING SOCIAL DIMENSIONS

IJCSES Vol.7 No.4 October 2013 pp.165-168 Serials Publications BEHAVIOR PERDITION VIA MINING SOCIAL DIMENSIONS V.Sudhakar 1 and G. Draksha 2 Abstract:- Collective behavior refers to the behaviors of individuals

### Adaptive Demand-Forecasting Approach based on Principal Components Time-series an application of data-mining technique to detection of market movement

Adaptive Demand-Forecasting Approach based on Principal Components Time-series an application of data-mining technique to detection of market movement Toshio Sugihara Abstract In this study, an adaptive

### Reputation Management Algorithms & Testing. Andrew G. West November 3, 2008

Reputation Management Algorithms & Testing Andrew G. West November 3, 2008 EigenTrust EigenTrust (Hector Garcia-molina, et. al) A normalized vector-matrix multiply based method to aggregate trust such

### 7 - Linear Transformations

7 - Linear Transformations Mathematics has as its objects of study sets with various structures. These sets include sets of numbers (such as the integers, rationals, reals, and complexes) whose structure

### COMPARATIVE EVALUATION OF UNCERTAINTY TR- ANSFORMATION FOR MEASURING COMPLEX-VALU- ED QUANTITIES

Progress In Electromagnetics Research Letters, Vol. 39, 141 149, 2013 COMPARATIVE EVALUATION OF UNCERTAINTY TR- ANSFORMATION FOR MEASURING COMPLEX-VALU- ED QUANTITIES Yu Song Meng * and Yueyan Shan National

### Implementation of Data Mining Techniques for Weather Report Guidance for Ships Using Global Positioning System

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 3 Issue. 3 Implementation of Data Mining Techniques for Weather Report Guidance for Ships Using Global Positioning System

### LOAD BALANCING AND EFFICIENT CLUSTERING FOR IMPROVING NETWORK PERFORMANCE IN AD-HOC NETWORKS

LOAD BALANCING AND EFFICIENT CLUSTERING FOR IMPROVING NETWORK PERFORMANCE IN AD-HOC NETWORKS Saranya.S 1, Menakambal.S 2 1 M.E., Embedded System Technologies, Nandha Engineering College (Autonomous), (India)

### A New Lower Bound for the Minimal Singular Value for Real Non-Singular Matrices by a Matrix Norm and Determinant

Applied Mathematical Sciences, Vol. 4, 2010, no. 64, 3189-3193 A New Lower Bound for the Minimal Singular Value for Real Non-Singular Matrices by a Matrix Norm and Determinant Kateřina Hlaváčková-Schindler

### 2.3 Scheduling jobs on identical parallel machines

2.3 Scheduling jobs on identical parallel machines There are jobs to be processed, and there are identical machines (running in parallel) to which each job may be assigned Each job = 1,,, must be processed

### Inner Product Spaces and Orthogonality

Inner Product Spaces and Orthogonality week 3-4 Fall 2006 Dot product of R n The inner product or dot product of R n is a function, defined by u, v a b + a 2 b 2 + + a n b n for u a, a 2,, a n T, v b,