Dissimilarity Representation For Pattern Recognition, The

Foundations And Applications

By: Elzbieta Pekalska, Robert P W Duin

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Hardcover | 7 December 2005

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636 Pages

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15.5 x 23.6 x 3.6

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This book provides a fundamentally new approach to pattern recognition in which objects are characterized by relations to other objects instead of by using features or models. This 'dissimilarity representation' bridges the gap between the traditionally opposing approaches of statistical and structural pattern recognition.Physical phenomena, objects and events in the world are related in various and often complex ways. Such relations are usually modeled in the form of graphs or diagrams. While this is useful for communication between experts, such representation is difficult to combine and integrate by machine learning procedures. However, if the relations are captured by sets of dissimilarities, general data analysis procedures may be applied for analysis.With their detailed description of an unprecedented approach absent from traditional textbooks, the authors have crafted an essential book for every researcher and systems designer studying or developing pattern recognition systems.

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Non-Fiction Computing & I.T.Computer Science Artificial Intelligence Computer Vision Pattern Recognition Booktopia Publisher Services World Scientific Publishing

Preface	p. vii
Notation and basic terminology	p. xi
Abbreviations	p. xix
Introduction	p. 1
Recognizing the pattern	p. 1
Dissimilarities for representation	p. 2
Learning from examples	p. 4
Motivation of the use of dissimilarity representations	p. 8
Relation to kernels	p. 13
Outline of the book	p. 14
In summary	p. 16
Spaces	p. 23
Preliminaries	p. 25
A brief look at spaces	p. 28
Generalized topological spaces	p. 32
Generalized metric spaces	p. 46
Vector spaces	p. 56
Normed and inner product spaces	p. 62
Reproducing kernel Hilbert spaces	p. 69
Indefinite inner product spaces	p. 71
Reproducing kernel Krein spaces	p. 85
Discussion	p. 87
Characterization of dissimilarities	p. 89
Embeddings, tree models and transformations	p. 90
Embeddings	p. 90
Distorted metric embeddings	p. 95
Tree models for dissimilarities	p. 95
Useful transformations	p. 99
Transformations in semimetric spaces	p. 99
Direct product spaces	p. 102
Invariance and robustness	p. 103
Properties of dissimilarity matrices	p. 105
Dissimilarity matrices	p. 105
Square distances and inner products	p. 116
Linear embeddings of dissimilarities	p. 118
Euclidean embedding	p. 118
Correction of non-Euclidean dissimilarities	p. 120
Pseudo-Euclidean embedding	p. 122
Generalized average variance	p. 124
Projecting new vectors to an embedded space	p. 125
Reduction of dimension	p. 127
Reduction of complexity	p. 128
A general embedding	p. 129
Spherical embeddings	p. 130
Spatial representation of dissimilarities	p. 132
FastMap	p. 133
Multidimensional scaling	p. 135
Reduction of complexity	p. 143
Summary	p. 144
Learning approaches	p. 147
Traditional learning	p. 148
Data bias and model bias	p. 148
Statistical learning	p. 151
Inductive principles	p. 154
Empirical risk minimization (ERM)	p. 156
Principles based on Occam's razor	p. 160
Why is the statistical approach not good enough for learning from objects?	p. 163
The role of dissimilarity representations	p. 166
Learned proximity representations	p. 171
Dissimilarity representations: learning	p. 172
Classification in generalized topological spaces	p. 175
Classification in dissimilarity spaces	p. 180
Characterization of dissimilarity spaces	p. 180
Classifiers	p. 185
Classification in pseudo-Euclidean spaces	p. 196
On generalized kernels and dissimilarity spaces	p. 205
Connection between dissimilarity spaces and pseudo-Euclidean spaces	p. 209
Discussion	p. 211
Dissimilarity measures	p. 215
Measures depending on feature types	p. 216
Measures between populations	p. 228
Normal distributions	p. 228
Divergence measures	p. 229
Discrete probability distributions	p. 233
Dissimilarity measures between sequences	p. 234
Information-theoretic measures	p. 237
Dissimilarity measures between sets	p. 238
Dissimilarity measures in applications	p. 242
Invariance and robustness	p. 242
Example measures	p. 242
Discussion and conclusions	p. 250
Visualization	p. 255
Multidimensional scaling	p. 257
First examples	p. 259
Linear and nonlinear methods: examples	p. 261
Implementation	p. 267
Other mappings	p. 268
Examples: getting insight into the data	p. 274
Tree models	p. 281
Summary	p. 287
Further data exploration	p. 289
Clustering	p. 290
Standard approaches	p. 290
Clustering on dissimilarity representations	p. 295
Clustering examples for dissimilarity representations	p. 303
Intrinsic dimension	p. 309
Sampling density	p. 319
Proposed criteria	p. 320
Experiments with the NIST digits	p. 325
Summary	p. 331
One-class classifiers	p. 333
General issues	p. 336
Construction of one-class classifiers	p. 337
One-class classifiers in feature spaces	p. 341
Domain descriptors for dissimilarity representations	p. 346
Neighborhood-based OCCs	p. 348
Generalized mean class descriptor	p. 350
Linear programming dissimilarity data description	p. 353
More issues on class descriptors	p. 359
Experiments	p. 366
Experiment I: Condition monitoring	p. 366
Experiment II: Diseased mucosa in the oral cavity	p. 374
Experiment III: Heart disease data	p. 377
Conclusions	p. 379
Classification	p. 383
Proof of principle	p. 384
NN rule vs alternative dissimilarity-based classifiers	p. 384
Experiment I: square dissimilarity representations	p. 388
Experiment II: the dissimilarity space approach	p. 389
Discussion	p. 395
Selection of the representation set: the dissimilarity space approach	p. 396
Prototype selection methods	p. 398
Experimental setup	p. 401
Results and discussion	p. 404
Conclusions	p. 416
Selection of the representation set: the embedding approach	p. 417
Prototype selection methods	p. 418
Experiments and results	p. 421
Conclusions	p. 428
On corrections of dissimilarity measures	p. 428
Going more Euclidean	p. 429
Experimental setup	p. 430
Results and conclusions	p. 432
A few remarks on a simulated missing value problem	p. 439
Existence of zero-error dissimilarity-based classifiers	p. 443
Asymptotic separability of classes	p. 444
Final discussion	p. 451
Combining	p. 453
Combining for one-class classification	p. 455
Combining strategies	p. 456
Data and experimental setup	p. 459
Results and discussion	p. 462
Summary and conclusions	p. 465
Combining for standard two-class classification	p. 466
Combining strategies	p. 466
Experiments on the handwritten digit set	p. 468
Results	p. 470
Conclusions	p. 473
Classifier projection space	p. 474
Construction and the use of CPS	p. 475
Summary	p. 483
Representation review and recommendations	p. 485
Representation review	p. 485
Three generalization ways	p. 486
Representation formation	p. 489
Generalization capabilities	p. 492
Practical considerations	p. 493
Clustering	p. 495
One-class classification	p. 496
Classification	p. 497
Conclusions and open problems	p. 503
Summary and contributions	p. 505
Extensions of dissimilarity representations	p. 508
Open questions	p. 510
On convex and concave functions	p. 515
Linear algebra in vector spaces	p. 519
Some facts on matrices in a Euclidean space	p. 519
Some facts on matrices in a pseudo-Euclidean space	p. 523
Measure and probability	p. 527
Statistical sidelines	p. 533
Likelihood and parameter estimation	p. 533
Expectation-maximization (EM) algorithm	p. 535
Model selection	p. 536
PCA and probabilistic models	p. 538
Gaussian model	p. 538
A Gaussian mixture model	p. 539
PCA	p. 541
Probabilistic PCA	p. 542
A mixture of probabilistic PCA	p. 543
Data sets	p. 545
Artificial data sets	p. 545
Real-world data sets	p. 549
Bibliography	p. 561
Index	p. 599
Table of Contents provided by Ingram. All Rights Reserved.

Dissimilarity Representation For Pattern Recognition, The

Foundations And Applications

At a Glance

Hardcover

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