The goal of this book is to present a variety of methods used in multidimensional data visualization. The emphasis is placed on new research results and trends in this field, including optimization, artificial neural networks, combinations of algorithms, parallel computing, different proximity measures, nonlinear manifold learning, and more. Many of the applications presented allow us to discover the obvious advantages of visual data mining--it is much easier for a decision maker to detect or extract useful information from graphical representation of data than from raw numbers.The fundamental idea of visualization is to provide data in some visual form that lets humans understand them, gain insight into the data, draw conclusions, and directly influence the process of decision making. Visual data mining is a field where human participation is integrated in the data analysis process; it covers data visualization and graphical presentation of information. Multidimensional Data Visualization is intended for scientists and researchers in any field of study where complex and multidimensional data must be visually represented. It may also serve as a useful research supplement for PhD students in operations research, computer science, various fields of engineering, as well as natural and social sciences. Read more... Multidimensional Data and the Concept of Visualization -- Strategies for Multidimensional Data Visualization -- Optimization-Based Visualization -- Combining Multidimensional Scaling with Artificial Neural Networks -- Applications of Visualization
Author(s): Gintautas Dzemyda; Olga Kurasova; J Žilinskas
Series: Springer optimization and its applications, v. 75
Publisher: Springer
Year: 2013
Language: English
Pages: 262
City: New York ; London
Tags: Информатика и вычислительная техника;Искусственный интеллект;Интеллектуальный анализ данных;
Cover......Page 1
Multidimensional DataVisualization......Page 4
Preface......Page 6
Contents......Page 8
Acronyms......Page 10
Notation......Page 12
1 Multidimensional Data and the Concept of Visualization......Page 14
2.1.1 Geometric Methods......Page 18
2.1.2 Iconographic Displays......Page 26
2.1.3 Hierarchical Displays......Page 27
2.2 Dimensionality Reduction......Page 28
2.2.1 Proximity Measures......Page 33
2.2.2 Principal Component Analysis......Page 34
2.2.3 Linear Discriminant Analysis......Page 39
2.2.4 Multidimensional Scaling......Page 40
2.2.4.1 SMACOF Algorithm......Page 41
2.2.4.2 Relative Mapping......Page 42
2.2.4.3 Sammon's Mapping......Page 43
2.2.5 Manifold-Based Visualization......Page 44
2.2.6 Isometric Feature Mapping......Page 45
2.2.7 Locally Linear Embedding......Page 48
2.3 Quantitative Criteria of Mapping......Page 51
2.3.1 Spearman's Coefficient......Page 52
2.3.2 König's Topology Preservation Measure......Page 53
3.1 Formulation of Optimization Problems in Multidimensional Scaling......Page 54
3.2 Differentiability Analysis of the Least Squares Stress Function......Page 57
3.3 Optimization Algorithms for Scaling......Page 60
3.4 Hybrid Evolutionary Algorithm for Multidimensional Scaling......Page 64
3.5 Two-Level Optimization of Stress with City-Block Distances......Page 67
3.5.1 Explicit Enumeration in Two-Level Optimization......Page 74
3.5.2 Branch-and-Bound Algorithm for MDS......Page 87
3.5.3 Combinatorial Evolutionary Algorithm......Page 101
3.6 Impact of Used Distance Measure on Visualization......Page 114
3.7 Impact of the Dimensionality of the Projection Space......Page 119
4.1 Feed-Forward Neural Networks in Visualization......Page 126
4.1.1 Biological Neuron and Its Artificial Model......Page 127
4.1.2 Artificial Neural Network Learning......Page 129
4.1.2.1 Perceptron......Page 130
4.1.2.2 Multilayer Feed-Forward Neural Networks......Page 132
4.1.2.3 Error Back-Propagation Learning Algorithm......Page 133
4.1.2.4 Network Testing......Page 134
4.1.3.1 Visualization Based on the Supervised Learning......Page 135
4.1.3.2 Auto-Associative Neural Network......Page 137
4.1.3.3 NeuroScale......Page 138
4.2 Self-Organizing Map and Neural Gas......Page 139
4.2.1 Principles of Self-Organizing Map......Page 140
4.2.2 SOM Training......Page 141
4.2.2.1 Properties of SOM Training......Page 143
4.2.4 Quality Measures of SOM and Neural Gas......Page 146
4.2.6 SOM for Multidimensional Data Visualization......Page 148
4.2.7 Comparative Analysis of SOM Software......Page 152
4.3.1.1 Investigation of Time Consumption......Page 158
4.3.1.2 SOM Combinations with Sammon's Mapping and SMACOF......Page 160
4.3.1.3 SOM and Neural Gas with SMACOF......Page 162
4.3.1.4 Examples of Visualization Using a Consecutive Combination......Page 164
4.3.2 Integrated Combination......Page 165
4.3.3.1 Combinations of SOM and Sammon's Mapping......Page 171
4.3.3.2 Combinations of SOM and NG with MDS......Page 176
4.3.3.3 Parallelization of the Integrated Combination SOM and NG with MDS......Page 179
4.4 Curvilinear Component Analysis......Page 181
4.5 The Feed-Forward Neural Network SAMANN......Page 183
4.5.1 Control of the Learning Rate......Page 187
4.5.2 Retraining of the SAMANN Network......Page 188
5.1.1 Economic and Social Conditions of Countries......Page 191
5.1.2 Qualitative Comparison of Schools......Page 194
5.2.1 Ophthalmological Data Analysis......Page 199
5.2.2 Analysis of Heart Rate Oscillations with Respect to Characterization of Sleep Stages......Page 202
5.2.3 Pharmacological Binding Affinity......Page 204
5.3.1 Theoretical and Methodological Background......Page 210
5.3.1.1 Experimental Investigation of Visual Presentation of a Set of Features......Page 214
5.3.2 Dimensionality Problem in the Visualization of Correlation-Based Data......Page 221
5.3.3 Environmental Data Analysis......Page 222
5.3.4 Visual Analysis of Curricula......Page 230
5.3.5 Analysis of Ophthalmological Features......Page 233
Appendix A: Test Data Sets......Page 239
References......Page 247
Index......Page 259
