## 23 Nov Read Chapter 8 in the textbook: Cluster Analysis Textbook: Tan, Pang-Ning. Introduction to Data Mining What are the characteristics of data? Compare the difference in each of the followin

Q1. Read Chapter 8 in the textbook: Cluster Analysis

**Textbook:** Tan, Pang-Ning. Introduction to Data Mining

- What are the characteristics of data?
- Compare the difference in each of the following clustering types: prototype-based, density-based, and graph-based.
- What is a scalable clustering algorithm?
- How do you choose the right algorithm?

Answer all the questions in Q&A format in 200 words. There must be APA formatted references (and APA in-text citations) to support the thoughts in the post.

Q2. Read ch. 8 in the textbook: Annotation

**Textbook:** Kirk, Andy. __Data Visualization: A Handbook for Data Driven Design__

Annotation is a crucial component of good data visualization. It can turn a boring graphic into an interesting and insightful way to convey information. This week, please navigate to any site and find a graphic that could use some annotation work. Add the graphic and the website it is found as an attachment and note what you would do to enhance the graphic and note why you would make these decisions.

Answer in 250 words.

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PANG.N I NG TAN Mich igan Sta te Un ivers i ty

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lsBN 0-321-42052-7

2 3 4 5 67 8 9 10-HAM-O8 07 06

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Preface

Advances in data generation and collection are producing data sets of mas- sive size in commerce and a variety of scientific disciplines. Data warehouses store details of the sales and operations of businesses, Earth-orbiting satellites beam high-resolution images and sensor data back to Earth, and genomics ex- periments generate sequence, structural, and functional data for an increasing number of organisms. The ease with which data can now be gathered and stored has created a new attitude toward data analysis: Gather whatever data you can whenever and wherever possible. It has become an article of faith that the gathered data will have value, either for the purpose that initially motivated its collection or for purposes not yet envisioned.

The field of data mining grew out of the limitations of current data anal- ysis techniques in handling the challenges posedl by these new types of data sets. Data mining does not replace other areas of data analysis, but rather takes them as the foundation for much of its work. While some areas of data mining, such as association analysis, are unique to the field, other areas, such as clustering, classification, and anomaly detection, build upon a long history of work on these topics in other fields. Indeed, the willingness of data mining researchers to draw upon existing techniques has contributed to the strength and breadth of the field, as well as to its rapid growth.

Another strength of the field has been its emphasis on collaboration with researchers in other areas. The challenges of analyzing new types of data cannot be met by simply applying data analysis techniques in isolation from those who understand the data and the domain in which it resides. Often, skill in building multidisciplinary teams has been as responsible for the success of data mining projects as the creation of new and innovative algorithms. Just as, historically, many developments in statistics were driven by the needs of agriculture, industry, medicine, and business, rxrany of the developments in data mining are being driven by the needs of those same fields.

This book began as a set of notes and lecture slides for a data mining course that has been offered at the University of Minnesota since Spring 1998 to upper-division undergraduate and graduate Students. Presentation slides

viii Preface

and exercises developed in these offerings grew with time and served as a basis for the book. A survey of clustering techniques in data mining, originally written in preparation for research in the area, served as a starting point for one of the chapters in the book. Over time, the clustering chapter was joined by chapters on data, classification, association analysis, and anomaly detection. The book in its current form has been class tested at the home institutions of the authors-the University of Minnesota and Michigan State University-as well as several other universities.

A number of data mining books appeared in the meantime, but were not completely satisfactory for our students primarily graduate and undergrad- uate students in computer science, but including students from industry and a wide variety of other disciplines. Their mathematical and computer back- grounds varied considerably, but they shared a common goal: to learn about data mining as directly as possible in order to quickly apply it to problems in their own domains. Thus, texts with extensive mathematical or statistical prerequisites were unappealing to many of them, as were texts that required a substantial database background. The book that evolved in response to these students needs focuses as directly as possible on the key concepts of data min- ing by illustrating them with examples, simple descriptions of key algorithms, and exercises.

Overview Specifically, this book provides a comprehensive introduction to data mining and is designed to be accessible and useful to students, instructors, researchers, and professionals. Areas covered include data preprocessing, vi- sualization, predictive modeling, association analysis, clustering, and anomaly detection. The goal is to present fundamental concepts and algorithms for each topic, thus providing the reader with the necessary background for the application of data mining to real problems. In addition, this book also pro- vides a starting point for those readers who are interested in pursuing research in data mining or related fields.

The book covers five main topics: data, classification, association analysis, clustering, and anomaly detection. Except for anomaly detection, each of these areas is covered in a pair of chapters. For classification, association analysis, and clustering, the introductory chapter covers basic concepts, representative algorithms, and evaluation techniques, while the more advanced chapter dis- cusses advanced concepts and algorithms. The objective is to provide the reader with a sound understanding of the foundations of data mining, while still covering many important advanced topics. Because of this approach, the book is useful both as a learning tool and as a reference.

Preface ix

To help the readers better understand the concepts that have been pre- sented, we provide an extensive set of examples, figures, and exercises. Bib- Iiographic notes are included at the end of each chapter for readers who are interested in more advanced topics, historically important papers, and recent trends. The book also contains a comprehensive subject and author index.

To the Instructor As a textbook, this book is suitable for a wide range of students at the advanced undergraduate or graduate level. Since students come to this subject with diverse backgrounds that may not include extensive knowledge of statistics or databases, our book requires minimal prerequisites- no database knowledge is needed and we assume only a modest background in statistics or mathematics. To this end, the book was designed to be as self-contained as possible. Necessary material from statistics, linear algebra, and machine learning is either integrated into the body of the text, or for some advanced topics, covered in the appendices.

Since the chapters covering major data mining topics are self-contained, the order in which topics can be covered is quite flexible. The core material is covered in Chapters 2, 4, 6, 8, and 10. Although the introductory data chapter (2) should be covered first, the basic classification, association analy- sis, and clustering chapters (4, 6, and 8, respectively) can be covered in any order. Because of the relationship of anomaly detection (10) to classification (4) and clustering (8), these chapters should precede Chapter 10. Various topics can be selected from the advanced classification, association analysis, and clustering chapters (5, 7, and 9, respectively) to fit the schedule and in- terests of the instructor and students. We also advise that the lectures be augmented by projects or practical exercises in data mining. Although they are time consuming, such hands-on assignments greatly enhance the value of the course.

Support Materials The supplements for the book are available at Addison- Wesley's Website www.aw.con/cssupport. Support materials available to all readers of this book include

PowerPoint lecture slides

Suggestions for student projects

Data mining resources such as data mining algorithms and data sets

On-line tutorials that give step-by-step examples for selected data mining techniques described in the book using actual data sets and data analysis software

o

o

o

o

x Preface

Additional support materials, including solutions to exercises, are available only to instructors adopting this textbook for classroom use. Please contact your school's Addison-Wesley representative for information on obtaining ac- cess to this material. Comments and suggestions, as well as reports of errors, can be sent to the authors through [email protected]

Acknowledgments Many people contributed to this book. We begin by acknowledging our families to whom this book is dedicated. Without their patience and support, this project would have been impossible.

We would like to thank the current and former students of our data mining groups at the University of Minnesota and Michigan State for their contribu- tions. Eui-Hong (Sam) Han and Mahesh Joshi helped with the initial data min- ing classes. Some ofthe exercises and presentation slides that they created can be found in the book and its accompanying slides. Students in our data min- ing groups who provided comments on drafts of the book or who contributed in other ways include Shyam Boriah, Haibin Cheng, Varun Chandola, Eric Eilertson, Levent Ertoz, Jing Gao, Rohit Gupta, Sridhar Iyer, Jung-Eun Lee, Benjamin Mayer, Aysel Ozgur, Uygar Oztekin, Gaurav Pandey, Kashif Riaz, Jerry Scripps, Gyorgy Simon, Hui Xiong, Jieping Ye, and Pusheng Zhang. We would also like to thank the students of our data mining classes at the Univer- sity of Minnesota and Michigan State University who worked with early drafbs of the book and provided invaluable feedback. We specifically note the helpful suggestions of Bernardo Craemer, Arifin Ruslim, Jamshid Vayghan, and Yu Wei.

Joydeep Ghosh (University of Texas) and Sanjay Ranka (University of Florida) class tested early versions of the book. We also received many useful suggestions directly from the following UT students: Pankaj Adhikari, Ra- jiv Bhatia, Fbederic Bosche, Arindam Chakraborty, Meghana Deodhar, Chris Everson, David Gardner, Saad Godil, Todd Hay, Clint Jones, Ajay Joshi, Joonsoo Lee, Yue Luo, Anuj Nanavati, Tyler Olsen, Sunyoung Park, Aashish Phansalkar, Geoff Prewett, Michael Ryoo, Daryl Shannon, and Mei Yang.

Ronald Kostoff (ONR) read an early version of the clustering chapter and offered numerous suggestions. George Karypis provided invaluable IATEX as- sistance in creating an author index. Irene Moulitsas also provided assistance with IATEX and reviewed some of the appendices. Musetta Steinbach was very helpful in finding errors in the figures.

We would like to acknowledge our colleagues at the University of Min- nesota and Michigan State who have helped create a positive environment for data mining research. They include Dan Boley, Joyce Chai, Anil Jain, Ravi

Preface xi

Janardan, Rong Jin, George Karypis, Haesun Park, William F. Punch, Shashi Shekhar, and Jaideep Srivastava. The collaborators on our many data mining projects, who also have our gratitude, include Ramesh Agrawal, Steve Can- non, Piet C. de Groen, FYan Hill, Yongdae Kim, Steve Klooster, Kerry Long, Nihar Mahapatra, Chris Potter, Jonathan Shapiro, Kevin Silverstein, Nevin Young, and Zhi-Li Zhang.

The departments of Computer Science and Engineering at the University of Minnesota and Michigan State University provided computing resources and a supportive environment for this project. ARDA, ARL, ARO, DOE, NASA, and NSF provided research support for Pang-Ning Tan, Michael Steinbach, and Vipin Kumar. In particular, Kamal Abdali, Dick Brackney, Jagdish Chan- dra, Joe Coughlan, Michael Coyle, Stephen Davis, Flederica Darema, Richard Hirsch, Chandrika Kamath, Raju Namburu, N. Radhakrishnan, James Sido- ran, Bhavani Thuraisingham, Walt Tiernin, Maria Zemankova, and Xiaodong Zhanghave been supportive of our research in data mining and high-performance computing.

It was a pleasure working with the helpful staff at Pearson Education. In particular, we would like to thank Michelle Brown, Matt Goldstein, Katherine Harutunian, Marilyn Lloyd, Kathy Smith, and Joyce Wells. We would also like to thank George Nichols, who helped with the art work and Paul Anag- nostopoulos, who provided I4.T[X support. We are grateful to the following Pearson reviewers: Chien-Chung Chan (University of Akron), Zhengxin Chen (University of Nebraska at Omaha), Chris Clifton (Purdue University), Joy- deep Ghosh (University of Texas, Austin), Nazli Goharian (Illinois Institute of Technology), J. Michael Hardin (University of Alabama), James Hearne (Western Washington University), Hillol Kargupta (University of Maryland, Baltimore County and Agnik, LLC), Eamonn Keogh (University of California- Riverside), Bing Liu (University of Illinois at Chicago), Mariofanna Milanova (University of Arkansas at Little Rock), Srinivasan Parthasarathy (Ohio State University), Zbigniew W. Ras (University of North Carolina at Charlotte), Xintao Wu (University of North Carolina at Charlotte), and Mohammed J. Zaki (Rensselaer Polvtechnic Institute).

Gontents

Preface

Introduction 1 1.1 What Is Data Mining? 2 7.2 Motivating Challenges 4 1.3 The Origins of Data Mining 6 1.4 Data Mining Tasks 7 1.5 Scope and Organization of the Book 11 1.6 Bibliographic Notes 13

vl l

t.7 Exercises

Data

16

19 2.I Types of Data 22

2.1.I Attributes and Measurement 23 2.L.2 Types of Data Sets . 29

2.2 Data Quality 36 2.2.I Measurement and Data Collection Issues 37 2.2.2 Issues Related to Applications

2.3 Data Preprocessing 2.3.L Aggregation 2.3.2 Sampling 2.3.3 Dimensionality Reduction 2.3.4 Feature Subset Selection 2.3.5 Feature Creation 2.3.6 Discretization and Binarization 2.3:7 Variable Tlansformation .

2.4 Measures of Similarity and Dissimilarity . . . 2.4.L Basics 2.4.2 Similarity and Dissimilarity between Simple Attributes . 2.4.3 Dissimilarities between Data Objects . 2.4.4 Similarities between Data Objects

43 44 45 47 50 52 55 57 63 65 66 67 69 72

xiv Contents

2.4.5 Examples of Proximity Measures 2.4.6 Issues in Proximity Calculation 2.4.7 Selecting the Right Proximity Measure

2.5 BibliographicNotes 2.6 Exercises

Exploring Data 3.i The Iris Data Set 3.2 Summary Statistics

3.2.L Frequencies and the Mode 3.2.2 Percentiles 3.2.3 Measures of Location: Mean and Median 3.2.4 Measures of Spread: Range and Variance 3.2.5 Multivariate Summary Statistics 3.2.6 Other Ways to Summarize the Data

3.3 Visualization 3.3.1 Motivations for Visualization 3.3.2 General Concepts 3.3.3 Techniques 3.3.4 Visualizing Higher-Dimensional Data . 3.3.5 Do's and Don'ts

3.4 OLAP and Multidimensional Data Analysis 3.4.I Representing Iris Data as a Multidimensional Array 3.4.2 Multidimensional Data: The General Case . 3.4.3 Analyzing Multidimensional Data 3.4.4 Final Comments on Multidimensional Data Analysis Bibliographic Notes Exercises

Classification: Basic Concepts, Decision Tlees, and Model Evaluation 4.1 Preliminaries 4.2 General Approach to Solving a Classification Problem 4.3 Decision Tlee Induction

4.3.1 How a Decision Tlee Works 4.3.2 How to Build a Decision TYee 4.3.3 Methods for Expressing Attribute Test Conditions 4.3.4 Measures for Selecting the Best Split . 4.3.5 Algorithm for Decision Tlee Induction 4.3.6 An Examole: Web Robot Detection

3.5 3.6

73 80 83 84 88

97 98 98 99

100 101 102 704 105 105 105 106 110 724 130 131 131 133 135 139 139 747

L45 746 748 150 150 151 155 158 164 166

Contents xv

4.3.7 Characteristics of Decision Tlee Induction 4.4 Model Overfitting

4.4.L Overfitting Due to Presence of Noise 4.4.2 Overfitting Due to Lack of Representative Samples 4.4.3 Overfitting and the Multiple Comparison Procedure 4.4.4 Estimation of Generalization Errors 4.4.5 Handling Overfitting in Decision Tlee Induction

4.5 Evaluating the Performance of a Classifier 4.5.I Holdout Method 4.5.2 Random Subsampling . . . 4.5.3 Cross-Validation 4.5.4 Bootstrap

4.6 Methods for Comparing Classifiers 4.6.L Estimating a Confidence Interval for Accuracy 4.6.2 Comparing the Performance of Two Models . 4.6.3 Comparing the Performance of Two Classifiers

4.7 BibliographicNotes 4.8 Exercises

5 Classification: Alternative Techniques 5.1 Rule-Based Classifier

5.1.1 How a Rule-Based Classifier Works 5.1.2 Rule-Ordering Schemes 5.1.3 How to Build a Rule-Based Classifier 5.1.4 Direct Methods for Rule Extraction 5.1.5 Indirect Methods for Rule Extraction 5.1.6 Characteristics of Rule-Based Classifiers

5.2 Nearest-Neighbor classifiers 5.2.L Algorithm 5.2.2 Characteristics of Nearest-Neighbor Classifiers

5.3 Bayesian Classifiers 5.3.1 Bayes Theorem 5.3.2 Using the Bayes Theorem for Classification 5.3.3 Naive Bayes Classifier 5.3.4 Bayes Error Rate 5.3.5 Bayesian Belief Networks

5.4 Artificial Neural Network (ANN) 5.4.I Perceptron 5.4.2 Multilayer Artificial Neural Network 5.4.3 Characteristics of ANN

168 172 L75 L77 178 179 184 186 186 187 187 188 188 189 191 192 193 198

207 207 209 2 I I 2r2 2r3 22L 223 223 225 226 227 228 229 23L 238 240 246 247 25r 255

xvi Contents

5.5 Support Vector Machine (SVM) 5.5.1 Maximum Margin Hyperplanes 5.5.2 Linear SVM: Separable Case 5.5.3 Linear SVM: Nonseparable Case 5.5.4 Nonlinear SVM . 5.5.5 Characteristics of SVM Ensemble Methods 5.6.1 Rationale for Ensemble Method 5.6.2 Methods for Constructing an Ensemble Classifier 5.6.3 Bias-Variance Decomposition 5.6.4 Bagging 5.6.5 Boosting 5.6.6 Random Forests 5.6.7 Empirical Comparison among Ensemble Methods Class Imbalance Problem 5.7.1 Alternative Metrics 5.7.2 The Receiver Operating Characteristic Curve 5.7.3 Cost-Sensitive Learning . . 5.7.4 Sampling-Based Approaches . Multiclass Problem Bibliographic Notes Exercises

5 .6

o . t

256 256 259 266 270 276 276 277 278 28r 283 285 290 294 294 295 298 302 305 306 309 315

c .6

5.9 5.10

Association Analysis: Basic Concepts and Algorithms 327 6.1 Problem Definition . 328 6.2 Flequent Itemset Generation 332

6.2.I The Apri,ori Principle 333 6.2.2 Fbequent Itemset Generation in the Apri,ori, Algorithm . 335 6.2.3 Candidate Generation and Pruning . . . 338 6.2.4 Support Counting 342 6.2.5 Computational Complexity 345

6.3 Rule Generatiorr 349 6.3.1 Confidence-Based Pruning 350 6.3.2 Rule Generation in Apri,ori, Algorithm 350 6.3.3 An Example: Congressional Voting Records 352

6.4 Compact Representation of Fbequent Itemsets 353 6.4.7 Maximal Flequent Itemsets 354 6.4.2 Closed Frequent Itemsets 355

6.5 Alternative Methods for Generating Frequent Itemsets 359 6.6 FP-Growth Alsorithm 363

Contents xvii

6.6.1 FP-tee Representation 6.6.2 Frequent Itemset Generation in FP-Growth Algorithm .

6.7 Evaluation of Association Patterns 6.7.l Objective Measures of Interestingness 6.7.2 Measures beyond Pairs of Binary Variables 6.7.3 Simpson's Paradox

6.8 Effect of Skewed Support Distribution 6.9 Bibliographic Notes

363 366 370 37r 382 384 386 390 404

4L5 415 4t8 418 422 424 426 429 429 431 436 439 442 443 444 447 448 453 457 457 458 458

460 461 463 465 469 473

6.10 Exercises

7 Association Analysis: Advanced 7.I Handling Categorical Attributes 7.2 Handling Continuous Attributes

Concepts

7.2.I Discretization-Based Methods 7.2.2 Statistics-Based Methods 7.2.3 Non-discretizalion Methods Handling a Concept Hierarchy Seouential Patterns 7.4.7 Problem Formulation 7.4.2 Sequential Pattern Discovery 7.4.3 Timing Constraints 7.4.4 Alternative Counting Schemes

7.5 Subgraph Patterns 7.5.1 Graphs and Subgraphs . 7.5.2 Frequent Subgraph Mining 7.5.3 Apri,od-like Method 7.5.4 Candidate Generation 7.5.5 Candidate Pruning 7.5.6 Support Counting

7.6 Infrequent Patterns 7.6.7 Negative Patterns 7.6.2 Negatively Correlated Patterns 7.6.3 Comparisons among Infrequent Patterns, Negative Pat-

terns, and Negatively Correlated Patterns 7.6.4 Techniques for Mining Interesting Infrequent Patterns 7.6.5 Techniques Based on Mining Negative Patterns 7.6.6 Techniques Based on Support Expectation .

7.7 Bibliographic Notes 7.8 Exercises

7.3 7.4

xviii Contents

Cluster Analysis: Basic Concepts and Algorithms 8.1 Overview

8.1.1 What Is Cluster Analysis? 8.I.2 Different Types of Clusterings . 8.1.3 Different Types of Clusters

8.2 K-means 8.2.7 The Basic K-means Algorithm 8.2.2 K-means: Additional Issues 8.2.3 Bisecting K-means 8.2.4 K-means and Different Types of Clusters 8.2.5 Strengths and Weaknesses 8.2.6 K-means as an Optimization Problem

8.3 Agglomerative Hierarchical Clustering 8.3.1 Basic Agglomerative Hierarchical Clustering Algorithm 8.3.2 Specific Techniques 8.3.3 The Lance-Williams Formula for Cluster Proximity . 8.3.4 Key Issues in Hierarchical Clustering . 8.3.5 Strengths and Weaknesses DBSCAN 8.4.1 Tladitional Density: Center-Based Approach 8.4.2 The DBSCAN Algorithm 8.4.3 Strengths and Weaknesses Cluster Evaluation 8.5.1 Overview 8.5.2 Unsupervised Cluster Evaluation Using Cohesion and

Separation 8.5.3 Unsupervised Cluster Evaluation Using the Proximity

Matrix 8.5.4 Unsupervised Evaluation of Hierarchical Clustering . 8.5.5 Determining the Correct Number of Clusters 8.5.6 Clustering Tendency 8.5.7 Supervised Measures of Cluster Validity 8.5.8 Assessing the Significance of Cluster Validity Measures .

8.4

8.5

487 490 490 49r 493 496 497 506 508 510 510 513 515 516 518 524 524 526 526 527 528 530 532 533

536

542 544 546 547 548 553 ooo

559 8.6 Bibliograph 8.7 Exercises

ic Notes

Cluster Analysis: Additional Issues and Algorithms 569 9.1 Characteristics of Data, Clusters, and Clustering Algorithms . 570

9.1.1 Example: Comparing K-means and DBSCAN . . . . . . 570 9.1.2 Data Characteristics 577

Contents xix

9.1.3 Cluster Characteristics . . 573 9.L.4 General Characteristics of Clustering Algorithms 575

9.2 Prototype-Based Clustering 577 9.2.1 Fzzy Clustering 577 9.2.2 Clustering Using Mixture Models 583 9.2.3 Self-Organizing Maps (SOM) 594

9.3 Density-Based Clustering 600 9.3.1 Grid-Based Clustering 601 9.3.2 Subspace Clustering 604 9.3.3 DENCLUE: A Kernel-Based Scheme for Density-Based

Clustering 608 9.4 Graph-Based Clustering 612

9.4.1 Sparsification 613 9.4.2 Minimum Spanning Tlee (MST) Clustering . . . 674 9.4.3 OPOSSUM: Optimal Partitioning of Sparse Similarities

Using METIS 616 9.4.4 Chameleon: Hierarchical Clustering with Dynamic

Modeling 9.4.5 Shared Nearest Neighbor Similarity 9.4.6 The Jarvis-Patrick Clustering Algorithm 9.4.7 SNN Density 9.4.8 SNN Density-Based Clustering

9.5 Scalable Clustering Algorithms 9.5.1 Scalability: General Issues and Approaches 9.5.2 BIRCH 9.5.3 CURE

9.6 Which Clustering Algorithm? 9.7 Bibliographic Notes 9.8 Exercises

616 622 625 627 629 630 630 633 635 639 643 647

10 Anomaly Detection 651 10.1 Preliminaries 653

10.1.1 Causes of Anomalies 653 10.1.2 Approaches to Anomaly Detection 654 10.1.3 The Use of Class Labels 655 10.1.4 Issues 656

10.2 Statistical Approaches 658 t0.2.7 Detecting Outliers in a Univariate Normal Distribution 659 10.2.2 Outl iersinaMult ivar iateNormalDistr ibut ion . . . . . 661 10.2.3 A Mixture Model Approach for Anomaly Detection. 662

xx Contents

10.2.4 Strengths and Weaknesses 10.3 Proximity-Based Outlier Detection

10.3.1 Strengths and Weaknesses 10.4 Density-Based Outlier Detection

10.4.1 Detection of Outliers Using Relative Density 70.4.2 Strengths and Weaknesses

10.5 Clustering-Based Techniques 10.5.1 Assessing the Extent to Which an Object Belongs to a

Cluster 10.5.2 Impact of Outliers on the Initial Clustering 10.5.3 The Number of Clusters to Use 10.5.4 Strengths and Weaknesses

665 666 666 668 669 670 67L

672 674 674 674 675 680

685 b6i)

10.6 Bibliograph 10.7 Exercises

ic Notes

Appendix A Linear Algebra A.1 Vectors

A.1.1 Definition 685 4.I.2 Vector Addition and Multiplication by a Scalar 685 A.1.3 Vector Spaces 687 4.7.4 The Dot Product, Orthogonality, and Orthogonal

Projections 688 A.1.5 Vectors and Data Analysis 690

42 Matrices 691 A.2.1 Matrices: Definitions 691 A-2.2 Matrices: Addition and Multiplication by a Scalar 692 4.2.3 Matrices: Multiplication 693 4.2.4 Linear tansformations and Inverse Matrices 695 4.2.5 Eigenvalue and Singular Value Decomposition . 697 4.2.6 Matrices and Data Analysis 699

A.3 Bibliographic Notes 700

Appendix B Dimensionality Reduction 7OL 8.1 PCA and SVD 70I

B.1.1 Principal Components Analysis (PCA) 70L 8.7.2 SVD . 706

8.2 Other Dimensionality Reduction Techniques 708 8.2.I Factor Analysis 708 8.2.2 Locally Linear Embedding (LLE) . 770 8.2.3 Multidimensional Scaling, FastMap, and ISOMAP 7I2

Contents xxi

8.2.4 Common Issues B.3 Bibliographic Notes

Appendix C Probability and Statistics C.1 Probability

C.1.1 Expected Values C.2 Statistics

C.2.L Point Estimation C.2.2 Central Limit Theorem C.2.3 Interval Estimation

C.3 Hypothesis Testing

Appendix D Regression D.1 Preliminaries D.2 Simple Linear Regression

D.2.L Least Square Method D.2.2 Analyzing Regression Errors D.2.3 Analyzing Goodness of Fit

D.3 Multivariate Linear Regression D.4 Alternative Least-Square Regression Methods

Appendix E Optimization E.1 Unconstrained Optimizafion

E.1.1 Numerical Methods 8.2 Constrained Optimization

E.2.I Equality Constraints 8.2.2 Inequality Constraints

Author Index

Subject Index

Copyright Permissions

715 7L6

7L9 7L9 722 723 724 724 725 726

739 739 742

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