COMPSTAT 2006 - Proceedings in Computational Statistics (eBook)

Preface 5
Contents 8
Part I Classification and Clustering 25
Issues of robustness and high dimensionality in cluster analysis 26
1 Introduction 26
2 Multivariate t Distribution 29
3 ML Estimation of Mixtures of t Components 30
4 Factor Analysis Model for Dimension Reduction 31
5 Mixtures of Normal Factor Analyzers 32
6 Mixtures of t Factor Analyzers 34
7 Discussion 36
References 36
Fuzzy K-medoids clustering models for fuzzy multivariate time trajectories 39
1 Introduction 39
2 Fuzzy data time arrays, fuzzy multivariate time trajectories and dissimilarity measures 40
3 Fuzzy K-means clustering models for fuzzy multivariate time trajectories [ CD03] 43
4 Fuzzy K-medoids clustering for fuzzy multivariate time trajectories 45
5 Application 47
References 50
Bootstrap methods for measuring classification uncertainty in latent class analysis 52
1 Introduction 52
2 Measures of classification uncertainty 54
3 The bootstrap method 55
4 Bootstrapping LC models 56
5 Applications 57
6 Discussion 60
References 61
A robust linear grouping algorithm 63
1 Introduction 63
2 Linear Grouping Algorithm 64
3 Robust Linear Grouping Algorithm 65
4 Examples 67
5 Discussion 70
References 72
Computing and using the deviance with classification trees 74
1 Introduction 74
2 Tree induction principle: an illustrative example 75
3 Validating the tree descriptive ability 77
4 Computational aspects 82
5 Conclusion 84
References 84
Estimation procedures for the false discovery rate: a systematic comparison for microarray data 86
1 Introduction 86
2 The testing problem 87
3 The false discovery rate 88
4 Estimation procedures 89
5 The data sets 92
6 Outline of the comparative study 95
7 Results and conclusions 96
Acknowledgment 98
References 98
A unifying model for biclustering* 99
1 Illustrative Example 99
2 Biclustering 100
3 A Unifying Biclustering Model 101
4 Data Analysis 103
5 Concluding Remarks 104
References 105
Part II Image Analysis and Signal Processing 107
Non-rigid image registration using mutual information 108
1 Introduction 108
2 Non-rigid registration 109
3 The mutual information criterion 112
4 Non-rigid registration using mutual information 113
5 Validation 116
References 117
Musical audio analysis using sparse representations 121
1 Introduction 121
2 Finding Sparse Representations 122
3 Sparse Representations for Music Transcription 125
4 Source Separation 128
5 Conclusions 130
Acknowledgements 130
References 131
Robust correspondence recognition for computer vision 134
1 Introduction 134
2 Stability and Digraph Kernels 138
3 Properties of Strict Sub-Kernels 142
4 A Simple Algorithm for Interval Orientations 144
5 Discussion 144
References 145
Blind superresolution 147
1 Introduction 147
2 Mathematical Model 150
3 Blind Superresolution 152
4 Experiments 155
5 Conclusions 156
Acknowledgment 157
References 157
Analysis of Music Time Series 160
1 Introduction 160
2 Model building 161
3 Applied models 164
4 Studies 166
5 Conclusion 171
References 172
Part III Data Visualization 173
Tying up the loose ends in simple, multiple, joint correspondence analysis 174
1 Introduction 174
2 Basic CA theory 175
3 Multiple and joint correspondence analysis 177
4 Data sets used as illustrations 177
5 Measuring variance and comparing different tables 178
6 The myth of the influential outlier 179
7 The scaling problem in CA 180
8 To rotate or not to rotate 186
9 Statistical significance of results 189
10 Loose ends in MCA and JCA 191
Acknowledgments 194
References 194
3 dimensional parallel coordinates plot and its use for variable selection 197
1 Introduction 197
2 Parallel coordinates plot and interactive operations 198
3 3 dimensional parallel coordinates plot 199
4 Implementation of 3D PCP software 203
5 Concluding remarks 204
References 204
Geospatial distribution of alcohol-related violence in Northern Virginia 206
1 Introduction 206
2 Overview of the Model 207
3 The Data 211
4 Estimating the Probabilities 212
5 Geospatial Visualization of Acute Outcomes 213
6 Conclusions 214
Acknowledgements 215
References 216
Visualization in comparative music research 217
1 Introduction 217
2 Music representations 218
3 Musical databases 219
4 Musical feature extraction 220
5 Data mining 220
6 Examples of visualization of musical collections 222
7 Conclusion 225
References 226
Exploratory modelling analysis: visualizing the value of variables 228
1 Introduction 228
2 Example — Florida 2004 229
3 Selection — More than just Variable Selection 231
4 Graphics for Variable Selection 233
5 Small or LARGE Datasets 236
6 Summary and Outlook 236
References 237
Density estimation from streaming data using wavelets 238
1 Introduction 238
2 Recursive Formulation 242
3 Discounting Old Data 243
4 A Case Study: Internet Header Traffic Data 245
References 249
Part IV Multivariate Analysis 250
Reducing conservatism of exact small-sample methods of inference for discrete data 251
1 Introduction 251
2 Small-Sample Inference for Discrete Distributions 253
3 Ways of Reducing Conservatism 255
4 Fuzzy Inference Using Discrete Data 259
5 The Mid-P Quasi-Exact Approach 260
Acknowledgement 264
References 265
Symbolic data analysis: what is it? 267
1 Symbolic Data 267
2 Structure 270
3 Analysis: Symbolic vis-a-vis Classical Approach 272
4 Conclusion 273
References 274
A dimensional reduction method for ordinal three- way contingency table 276
1 Introduction 276
2 Decomposing a Non Symmetric Index 277
3 The Partition of a Predictability Measure 279
4 Ordinal Three-Way Non Symmetrical Correspondence Analysis 280
5 Example 284
References 287
Operator related to a data matrix: a survey 289
1 The initial choices 289
2 Joint analysis of several data matrices (the STATIS method) 293
3 Principal component analysis with respect to instrumental variables 295
4 Conclusions 298
Acknowledgements 299
References 299
Factor interval data analysis and its application 302
1 Introduction 302
2 Methodology of Interval Data and Its Possible Limitations 303
3 Methodology of Factor Interval Data and Its Advantages 307
4 Application in Chinese Stock Markets 309
5 Conclusion 315
References 315
Identifying excessively rounded or truncated data 316
1 Data 316
2 DensityModels 317
3 Asymptotic Behavior 322
4 Conclusion 325
Acknowledgements 325
References 326
Statistical inference and data mining: false discoveries control 327
Introduction 327
1 Data Mining Specificities and Statistical Inference 328
2 Validation of Interesting Features 329
3 Controlling UAFWER Using the BS FD Algorithm 332
4 Experimentation 335
Conclusion and Perspectives 337
References 337
Is ‘Which model . . .?’ the right question? 339
1 Introduction 339
2 Preliminaries 340
3 From choice to synthesis 342
4 Example 347
5 Conclusion 350
References 350
Use of latent class regression models with a random intercept to remove the effects of the overall response rating level 352
1 Introduction 352
2 Description of the cracker case study 353
3 The LC ordinal regression model with a random intercept 354
4 Results obtained with the cracker data set 356
5 General discussion 357
References 360
Discrete functional data analysis 362
1 Introduction 362
2 Functional Data 363
3 Difference Operators 363
4 Detection of Relations among Differences 365
5 Concluding Remarks 369
References 369
Self organizing MAPS: understanding, measuring and reducing variability 371
1 Introduction 372
2 Several Approaches Concerning the Preservation of the Topology 373
3 Understanding Variability of SOM’ Neighbourhood Structure Visualizing Distances between All Classes 375
4 The R-map Method to Increase SOM Reliability 376
5 Application: Validating the Number of Units for a SOM Network 379
6 Conclusion 381
References 382
Parameterization and estimation of path models for categorical data 383
1 Introduction 383
2 Log-linear, graphical and DAG models 384
3 DAG models as marginal models 386
4 Parameterization of DAG models 386
5 Path models 387
6 Maximum likelihood estimation 388
7 An example 390
References 394
Latent class model with two latent variables for analysis of count data 395
1 Introduction 395
2 Model 396
3 Analysis of retail market data 397
References 399
Part V Web Based Teaching 400
Challenges concerning web data mining 401
1 Motivation 401
2 Challenges Concerning Algorithmic Aspects 405
3 Conclusions and Further Research 412
References 412
e-Learning statistics – a selective review 415
1 Introduction 415
2 Modern e-Learning Materials 416
3 Evaluation 423
4 Conclusion 424
References 425
Quality assurance of web based e-Learning for statistical education 427
1 Introduction 427
2 Important Features of the e-StatEdu System 429
3 Quality Assurance 432
4 Discussion 435
Acknowledgement 435
References 435
Part VI Algorithms 437
Genetic algorithms for building double threshold generalized autoregressive conditional heteroscedastic models of time series 438
1 Introduction 439
2 The DTGARCHModel 441
3 A Genetic Algorithm for DTGARCH Model Building 442
4 Application to Financial Data 444
5 Conclusions 447
References 448
Nonparametric evaluation of matching noise 450
1 Introduction and preliminaries 450
2 Statistical framework for matching noise 451
3 Matching noise for KNN distance hot-deck 453
4 An important special case: distance hot-deck 454
5 d0-Kernel hot-deck 455
6 A comparison among different techniques 456
References 457
Subset selection algorithm based on mutual information 458
1 Introduction 458
2 Estimation of mutual information using normal mixture 460
3 Algorithm for subset selection 461
4 Numerical investigation with real data set 465
References 465
Visiting near-optimal solutions using local search algorithms 468
1 Background and motivation 468
2 Definitions and notation 469
3 The ß-acceptable solution probability 471
4 Visiting a ß-acceptable solution 473
5 Computational results 474
6 Conclusions 477
References 478
The convergence of optimization based GARCH estimators: theory and application* 479
1 Introduction 479
2 Convergence of Optimization Based Estimators 480
3 Application to GARCH Model 483
4 Results 484
5 Conclusions 488
References 489
The stochastics of threshold accepting: analysis of an application to the uniform design problem 491
1 Introduction 491
2 Formal Framework 492
3 Results for Uniform Design Implementation 493
4 Conclusions and Outlook 498
References 498
Part VII Robustness 500
Robust classification with categorical variables 501
1 Introduction 501
2 Cluster detection through diagnostic monitoring 502
3 Performance of the method 505
4 E-government data 509
Acknowledgement 512
References 512
Multiple group linear discriminant analysis: robustness and error rate 514
1 Introduction 514
2 Estimation and Robustness 516
3 Optimal Error Rate for Three Groups 518
4 Simulations 520
5 Conclusions 524
References 524
Author Index 526