This book is a comprehensive introduction to the methods and algorithms of modern data analytics. It provides a sound mathematical basis, discusses advantages and drawbacks of different approaches, and enables the reader to design and implement data analytics solutions for real-world applications. This book has been used for more than ten years in the Data Mining course at the Technical University of Munich. Much of the content is based on the results of industrial research and development projects at Siemens. Content • Data Analytics • Data and Relations • Data Preprocessing • Data Visualization • Correlation • Regression • Forecasting • Classification • Clustering Target Groups Students of computer science, mathematics and engineering Data analytics practitioners The Author Thomas A. Runkler is Principal Research Scientist at Siemens Corporate Technology and Professor for Computer Science at the Technical University of Munich Preface 5 Contents 7 List of Symbols 10 1 Introduction 12 1.1 It's All About Data 12 1.2 Data Analytics, Data Mining, and Knowledge Discovery 13 References 14 2 Data and Relations 16 2.1 The Iris Data Set 16 2.2 Data Scales 19 2.3 Set and Matrix Representations 21 2.4 Relations 22 2.5 Dissimilarity Measures 22 2.6 Similarity Measures 25 2.7 Sequence Relations 27 2.8 Sampling and Quantization 29 Problems 32 References 33 3 Data Preprocessing 34 3.1 Error Types 34 3.2 Error Handling 37 3.3 Filtering 38 3.4 Data Transformation 44 3.5 Data Integration 46 Problems 47 References 47 4 Data Visualization 48 4.1 Diagrams 48 4.2 Principal Component Analysis 50 4.3 Multidimensional Scaling 54 4.4 Sammon Mapping 58 4.5 Auto-encoder 62 4.6 Histograms 62 4.7 Spectral Analysis 65 Problems 69 References 70 5 Correlation 71 5.1 Linear Correlation 71 5.2 Correlation and Causality 73 5.3 Chi-Square Test for Independence 74 Problems 77 References 78 6 Regression 79 6.1 Linear Regression 79 6.2 Linear Regression with Nonlinear Substitution 84 6.3 Robust Regression 84 6.4 Neural Networks 85 6.5 Radial Basis Function Networks 91 6.6 Cross-Validation 92 6.7 Feature Selection 95 Problems 96 References 97 7 Forecasting 98 7.1 Finite State Machines 98 7.2 Recurrent Models 100 7.3 Autoregressive Models 101 Problems 102 References 103 8 Classification 104 8.1 Classification Criteria 104 8.2 Naive Bayes Classifier 108 8.3 Linear Discriminant Analysis 111 8.4 Support Vector Machine 113 8.5 Nearest Neighbor Classifier 115 8.6 Learning Vector Quantization 116 8.7 Decision Trees 117 Problems 122 References 123 9 Clustering 125 9.1 Cluster Partitions 125 9.2 Sequential Clustering 127 9.3 Prototype-Based Clustering 129 9.4 Fuzzy Clustering 131 9.5 Relational Clustering 137 9.6 Cluster Tendency Assessment 141 9.7 Cluster Validity 142 9.8 Self-organizing Map 143 Problems 145 References 145 A Brief Review of Some Optimization Methods 148 A.1 Optimization with Derivatives 148 A.2 Gradient Descent 149 A.3 Lagrange Optimization 150 References 152 Solutions 153 Problems of Chapter 2 153 Problems of Chapter 3 154 Problems of Chapter 4 154 Problems of Chapter 5 155 Problems of Chapter 6 156 Problems of Chapter 7 157 Problems of Chapter 8 158 Problems of Chapter 9 159 Index 161
