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Generalized Principal Component Analysis 1st ed. 2016 [Kietas viršelis]

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  • Formatas: Hardback, 566 pages, aukštis x plotis: 235x155 mm, weight: 1057 g, 83 Illustrations, color; 38 Illustrations, black and white; XXXII, 566 p. 121 illus., 83 illus. in color., 1 Hardback
  • Serija: Interdisciplinary Applied Mathematics 40
  • Išleidimo metai: 12-Apr-2016
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 0387878106
  • ISBN-13: 9780387878102
Kitos knygos pagal šią temą:
Generalized Principal Component Analysis 1st ed. 2016Didesnis paveikslėlis
  • Formatas: Hardback, 566 pages, aukštis x plotis: 235x155 mm, weight: 1057 g, 83 Illustrations, color; 38 Illustrations, black and white; XXXII, 566 p. 121 illus., 83 illus. in color., 1 Hardback
  • Serija: Interdisciplinary Applied Mathematics 40
  • Išleidimo metai: 12-Apr-2016
  • Leidėjas: Springer-Verlag New York Inc.
  • ISBN-10: 0387878106
  • ISBN-13: 9780387878102
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780387878102.html
Raktažodžiai:
This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc.

This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book.





René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. 

Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.

Recenzijos

The book under review provides a timely and comprehensive description of the classic and modern PCA-based and other dimension reduction techniques. Although the topic of dimension reduction has been briefly converted in quite a few books and review papers, this book should be especially applauded for its unique depth and comprehensiveness. Overall, this is one of the best books on PCA and modern dimension reduction techniques and should expect an increasing popularity. (Steven (Shuangge) Ma, Mathematical Reviews, January, 2017)

1 Introduction
1(24)
1.1 Modeling Data with a Parametric Model
2(4)
1.1.1 The Choice of a Model Class
3(1)
1.1.2 Statistical Models versus Geometric Models
4(2)
1.2 Modeling Mixed Data with a Mixture Model
6(10)
1.2.1 Examples of Mixed Data Modeling
7(5)
1.2.2 Mathematical Representations of Mixture Models
12(4)
1.3 Clustering via Discriminative or Nonparametric Methods
16(2)
1.4 Noise, Errors, Outliers, and Model Selection
18(7)
Part I Modeling Data with a Single Subspace
2 Principal Component Analysis
25(38)
2.1 Classical Principal Component Analysis (PCA)
25(13)
2.1.1 A Statistical View of PCA
26(4)
2.1.2 A Geometric View of PCA
30(4)
2.1.3 A Rank Minimization View of PCA
34(4)
2.2 Probabilistic Principal Component Analysis (PPCA)
38(7)
2.2.1 PPCA from Population Mean and Covariance
39(1)
2.2.2 PPCA by Maximum Likelihood
40(5)
2.3 Model Selection for Principal Component Analysis
45(8)
2.3.1 Model Selection by Information-Theoretic Criteria
46(3)
2.3.2 Model Selection by Rank Minimization
49(2)
2.3.3 Model Selection by Asymptotic Mean Square Error
51(2)
2.4 Bibliographic Notes
53(1)
2.5 Exercises
54(9)
3 Robust Principal Component Analysis
63(60)
3.1 PCA with Robustness to Missing Entries
64(23)
3.1.1 Incomplete PCA by Mean and Covariance Completion
68(1)
3.1.2 Incomplete PPCA by Expectation Maximization
69(4)
3.1.3 Matrix Completion by Convex Optimization
73(5)
3.1.4 Incomplete PCA by Alternating Minimization
78(9)
3.2 PCA with Robustness to Corrupted Entries
87(12)
3.2.1 Robust PCA by Iteratively Reweighted Least Squares
89(3)
3.2.2 Robust PCA by Convex Optimization
92(7)
3.3 PCA with Robustness to Outliers
99(14)
3.3.1 Outlier Detection by Robust Statistics
101(6)
3.3.2 Outlier Detection by Convex Optimization
107(6)
3.4 Bibliographic Notes
113(2)
3.5 Exercises
115(8)
4 Nonlinear and Nonparametric Extensions
123(48)
4.1 Nonlinear and Kernel PCA
126(7)
4.1.1 Nonlinear Principal Component Analysis (NLPCA)
126(2)
4.1.2 NLPCA in a High-dimensional Feature Space
128(1)
4.1.3 Kernel PCA (KPCA)
129(4)
4.2 Nonparametric Manifold Learning
133(10)
4.2.1 Multidimensional Scaling (MDS)
134(1)
4.2.2 Locally Linear Embedding (LLE)
135(3)
4.2.3 Laplacian Eigenmaps (LE)
138(5)
4.3 K-Means and Spectral Clustering
143(17)
4.3.1 K-Means Clustering
145(3)
4.3.2 Spectral Clustering
148(12)
4.4 Bibliographic Notes
160(1)
4.5 Exercises
161(5)
4.A Laplacian Eigenmaps: Continuous Formulation
166(5)
Part II Modeling Data with Multiple Subspaces
5 Algebraic-Geometric Methods
171(46)
5.1 Problem Formulation of Subspace Clustering
172(4)
5.1.1 Projectivization of Affine Subspaces
172(2)
5.1.2 Subspace Projection and Minimum Representation
174(2)
5.2 Introductory Cases of Subspace Clustering
176(8)
5.2.1 Clustering Points on a Line
176(3)
5.2.2 Clustering Lines in a Plane
179(2)
5.2.3 Clustering Hyperplanes
181(3)
5.3 Subspace Clustering Knowing the Number of Subspaces
184(12)
5.3.1 An Introductory Example
184(2)
5.3.2 Fitting Polynomials to Subspaces
186(2)
5.3.3 Subspaces from Polynomial Differentiation
188(2)
5.3.4 Point Selection via Polynomial Division
190(3)
5.3.5 The Basic Algebraic Subspace Clustering Algorithm
193(3)
5.4 Subspace Clustering not Knowing the Number of Subspaces
196(5)
5.4.1 Introductory Examples
196(2)
5.4.2 Clustering Subspaces of Equal Dimension
198(2)
5.4.3 Clustering Subspaces of Different Dimensions
200(1)
5.5 Model Selection for Multiple Subspaces
201(6)
5.5.1 Effective Dimension of Samples of Multiple Subspaces
202(2)
5.5.2 Minimum Effective Dimension of Noisy Samples
204(1)
5.5.3 Recursive Algebraic Subspace Clustering
205(2)
5.6 Bibliographic Notes
207(3)
5.7 Exercises
210(7)
6 Statistical Methods
217(50)
6.1 K-Subspaces
219(3)
6.1.1 K-Subspaces Model
219(1)
6.1.2 K-Subspaces Algorithm
220(1)
6.1.3 Convergence of the K-Subspaces Algorithm
221(1)
6.1.4 Advantages and Disadvantages of K-Subspaces
222(1)
6.2 Mixture of Probabilistic PCA (MPPCA)
222(9)
6.2.1 MPPCA Model
223(1)
6.2.2 Maximum Likelihood Estimation for MPPCA
223(3)
6.2.3 Maximum a Posteriori (MAP) Estimation for MPPCA
226(2)
6.2.4 Relationship between K-Subspaces and MPPCA
228(3)
6.3 Compression-Based Subspace Clustering
231(16)
6.3.1 Model Estimation and Data Compression
231(2)
6.3.2 Minimium Coding Length via Agglomerative Clustering
233(5)
6.3.3 Lossy Coding of Multivariate Data
238(4)
6.3.4 Coding Length of Mixed Gaussian Data
242(5)
6.4 Simulations and Applications
247(11)
6.4.1 Statistical Methods on Synthetic Data
247(7)
6.4.2 Statistical Methods on Gene Expression Clustering, Image Segmentation, and Face Clustering
254(4)
6.5 Bibliographic Notes
258(3)
6.6 Exercises
261(2)
6.A Lossy Coding Length for Subspace-like Data
263(4)
7 Spectral Methods
267(24)
7.1 Spectral Subspace Clustering
268(2)
7.2 Local Subspace Affinity (LSA) and Spectral Local Best-Fit Flats (SLBF)
270(4)
7.3 Locally Linear Manifold Clustering (LLMC)
274(2)
7.4 Spectral Curvature Clustering (SCC)
276(3)
7.5 Spectral Algebraic Subspace Clustering (SASC)
279(2)
7.6 Simulations and Applications
281(8)
7.6.1 Spectral Methods on Synthetic Data
281(4)
7.6.2 Spectral Methods on Face Clustering
285(4)
7.7 Exercises
289(2)
8 Sparse and Low-Rank Methods
291(58)
8.1 Self-Expressiveness and Subspace-Preserving Representations
294(3)
8.1.1 Self-Expressiveness Property
294(2)
8.1.2 Subspace-Preserving Representation
296(1)
8.2 Low-Rank Subspace Clustering (LRSC)
297(13)
8.2.1 LRSC with Uncorrupted Data
297(5)
8.2.2 LRSC with Robustness to Noise
302(6)
8.2.3 LRSC with Robustness to Corruptions
308(2)
8.3 Sparse Subspace Clustering (SSC)
310(23)
8.3.1 SSC with Uncorrupted Data
310(14)
8.3.2 SSC with Robustness to Outliers
324(2)
8.3.3 SSC with Robustness to Noise
326(4)
8.3.4 SSC with Robustness to Corrupted Entries
330(2)
8.3.5 SSC for Affine Subspaces
332(1)
8.4 Simulations and Applications
333(11)
8.4.1 Low-Rank and Sparse Methods on Synthetic Data
333(3)
8.4.2 Low-Rank and Sparse Methods on Face Clustering
336(8)
8.5 Bibliographic Notes
344(1)
8.6 Exercises
345(4)
Part III Applications
9 Image Representation
349(28)
9.1 Seeking Compact and Sparse Image Representations
349(5)
9.1.1 Prefixed Linear Transformations
350(1)
9.1.2 Adaptive, Overcomplete, and Hybrid Representations
351(2)
9.1.3 Hierarchical Models for Multiscale Structures.
353(1)
9.2 Image Representation with Multiscale Hybrid Linear Models
354(15)
9.2.1 Linear versus Hybrid Linear Models
354(7)
9.2.2 Multiscale Hybrid Linear Models
361(4)
9.2.3 Experiments and Comparisons
365(4)
9.3 Multiscale Hybrid Linear Models in Wavelet Domain
369(7)
9.3.1 Imagery Data Vectors in the Wavelet Domain
369(2)
9.3.2 Hybrid Linear Models in the Wavelet Domain
371(1)
9.3.3 Comparison with Other Lossy Representations
372(4)
9.4 Bibliographic Notes
376(1)
10 Image Segmentation
377(24)
10.1 Basic Models and Principles
378(4)
10.1.1 Problem Formulation
378(2)
10.1.2 Image Segmentation as Subspace Clustering
380(1)
10.1.3 Minimum Coding Length Principle
381(1)
10.2 Encoding Image Textures and Boundaries
382(4)
10.2.1 Construction of Texture Features
382(1)
10.2.2 Texture Encoding
383(1)
10.2.3 Boundary Encoding
384(2)
10.3 Compression-Based Image Segmentation
386(6)
10.3.1 Minimizing Total Coding Length
386(1)
10.3.2 Hierarchical Implementation
387(2)
10.3.3 Choosing the Proper Distortion Level
389(3)
10.4 Experimental Evaluation
392(7)
10.4.1 Color Spaces and Compressibility
392(2)
10.4.2 Experimental Setup
394(1)
10.4.3 Results and Discussions
395(4)
10.5 Bibliographic Notes
399(2)
11 Motion Segmentation
401(30)
11.1 The 3D Motion Segmentation Problem
402(3)
11.2 Motion Segmentation from Multiple Affine Views
405(8)
11.2.1 Affine Projection of a Rigid-Body Motion
405(1)
11.2.2 Motion Subspace of a Rigid-Body Motion
406(1)
11.2.3 Segmentation of Multiple Rigid-Body Motions
406(1)
11.2.4 Experiments on Multiview Motion Segmentation
407(6)
11.3 Motion Segmentation from Two Perspective Views
413(8)
11.3.1 Perspective Projection of a Rigid-Body Motion
414(1)
11.3.2 Segmentation of 3D Translational Motions
415(1)
11.3.3 Segmentation of Rigid-Body Motions
416(1)
11.3.4 Segmentation of Rotational Motions or Planar Scenes
417(1)
11.3.5 Experiments on Two-View Motion Segmentation
418(3)
11.4 Temporal Motion Segmentation
421(7)
11.4.1 Dynamical Models of Time-Series Data
422(1)
11.4.2 Experiments on Temporal Video Segmentation
423(2)
11.4.3 Experiments on Segmentation of Human Motion Data
425(3)
11.5 Bibliographical Notes
428(3)
12 Hybrid System Identification
431(22)
12.1 Problem Statement
433(1)
12.2 Identification of a Single ARX System
434(4)
12.3 Identification of Hybrid ARX Systems
438(8)
12.3.1 The Hybrid Decoupling Polynomial
439(1)
12.3.2 Identifying the Hybrid Decoupling Polynomial
440(3)
12.3.3 Identifying System Parameters and Discrete States
443(2)
12.3.4 The Basic Algorithm and Its Extensions
445(1)
12.4 Simulations and Experiments
446(4)
12.4.1 Error in the Estimation of the Model Parameters
447(1)
12.4.2 Error as a Function of the Model Orders
447(1)
12.4.3 Error as a Function of Noise
448(1)
12.4.4 Experimental Results on Test Data Sets
449(1)
12.5 Bibliographic Notes
450(3)
13 Final Words
453(8)
13.1 Unbalanced and Multimodal Data
454(1)
13.2 Unsupervised and Semisupervised Learning
454(1)
13.3 Data Acquisition and Online Data Analysis
455(1)
13.4 Other Low-Dimensional Models
456(1)
13.5 Computability and Scalability
457(2)
13.6 Theory, Algorithms, Systems, and Applications
459(2)
A Basic Facts from Optimization 461(14)
A.1 Unconstrained Optimization
461(7)
A.1.1 Optimality Conditions
462(1)
A.1.2 Convex Set and Convex Function
462(2)
A.1.3 Subgradient
464(1)
A.1.4 Gradient Descent Algorithm
465(1)
A.1.5 Alternating Direction Minimization
466(2)
A.2 Constrained Optimization
468(6)
A.2.1 Optimality Conditions and Lagrangian Multipliers
468(2)
A.2.2 Augmented Lagrange Multipler Methods
470(1)
A.2.3 Alternating Direction Method of Multipliers
471(3)
A.3 Exercises
474(1)
B Basic Facts from Mathematical Statistics 475(34)
B.1 Estimation of Parametric Models
475(10)
B.1.1 Sufficient Statistics
476(1)
B.1.2 Mean Square Error, Efficiency, and Fisher Information
477(2)
B.1.3 The Rao—Blackwell Theorem and Uniformly Minimum-Variance Unbiased Estimator
479(1)
B.1.4 Maximum Likelihood (ML) Estimator
480(1)
B.1.5 Consistency and Asymptotic Efficiency of the ML Estimator
481(4)
B.2 ML Estimation for Models with Latent Variables
485(5)
B.2.1 Expectation Maximization (EM)
486(2)
B.2.2 Maximum a Posteriori Expectation Maximization (MAP-EM)
488(2)
B.3 Estimation of Mixture Models
490(6)
B.3.1 EM for Mixture Models
490(2)
B.3.2 MAP-EM for Mixture Models
492(2)
B.3.3 A Case in Which EM Fails
494(2)
B.4 Model-Selection Criteria
496(2)
B.4.1 Akaike Information Criterion
497(1)
B.4.2 Bayesian Information Criterion
498(1)
B.5 Robust Statistical Methods
498(8)
B.5.1 Influence-Based Outlier Detection
499(2)
B.5.2 Probability-Based Outlier Detection
501(2)
B.5.3 Random-Sampling-Based Outlier Detection
503(3)
B.6 Exercises
506(3)
C Basic Facts from Algebraic Geometry 509(26)
C.1 Abstract Algebra Basics
509(10)
C.1.1 Polynomial Rings
509(2)
C.1.2 Ideals and Algebraic Sets
511(2)
C.1.3 Algebra and Geometry: Hilbert's Nullstellensatz
513(1)
C.1.4 Algebraic Sampling Theory
514(2)
C.1.5 Decomposition of Ideals and Algebraic Sets
516(1)
C.1.6 Hilbert Function, Polynomial, and Series
517(2)
C.2 Ideals of Subspace Arrangements
519(3)
C.3 Subspace Embedding and PL-Generated Ideals
522(2)
C.4 Hilbert Functions of Subspace Arrangements
524(10)
C.4.1 Hilbert Function and Algebraic Subspace Clustering
525(3)
C.4.2 Special Cases of the Hilbert Function
528(2)
C.4.3 Formulas for the Hilbert Function
530(4)
C.5 Bibliographic Notes
534(1)
References 535(18)
Index 553
René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University.

Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University.

S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.