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Tables of Contents for Advances in Independent Component Analysis
Chapter/Section Title
Page #
Page Count
Contributors
xv
Foreword
xix
Part I Temporal ICA Models
Hidden Markov Independent Component Analysis
3
20
William D. Penny
Richard M. Everson
Stephen J. Roberts
Introduction
3
1
Hidden Markov Models
3
3
Independent Component Analysis
6
2
Generalised Exponential Sources
6
1
Generalised Autoregressive Sources
7
1
Hidden Markov ICA
8
2
Generalised Exponential Sources
9
1
Generalised Autoregressive Sources
10
1
Practical Issues
10
2
Initialisation
10
1
Learning
10
2
Model Order Selection
12
1
Results
12
7
Multiple Sinewave Sources
12
2
Same Sources, Different Mixing
14
2
Same Mixing, Different Sources
16
1
EEG Data
16
3
Conclusion
19
1
Acknowledgements
20
1
Appendix
20
3
Particle Filters for Non-Stationary ICA
23
22
Richard M. Everson
Stephen J. Roberts
Introduction
23
1
Stationary ICA
23
2
Non-Stationary Independent Component Analysis
25
3
Source Model
27
1
Particle Filters
28
2
Source Recovery
29
1
Illustration of Non-Stationary ICA
30
3
Smoothing
33
3
Temporal Correlations
36
2
Conclusion
38
1
Acknowledgement
38
1
Appendix: Laplace's Approximation for the Likelihood
39
6
Part II The Validity of the Independence Assumption
The Independence Assumption; Analyzing the Independence of the Components by Topography
45
18
Aapo Hyvarinen
Patrik O. Hoyer
Mika Inki
Introduction
45
2
Background: Independent's Subspace Analysis
47
2
Topographic ICA Model
49
4
Dependence and Topography
49
1
Defining Topographic ICA
50
1
The Generative Model
51
1
Basic Properties of the Topographic ICA Model
52
1
Learning Rule
53
1
Comparison with Other Topographic Mappings
54
1
Experiment
55
4
Experiments in Feature Extraction of Image Data
55
2
Experiments in Feature Extraction of Audio Data
57
1
Experiments with Magnetoencephalographic Recordings
58
1
Conclusion
59
4
The Independence Assumption: Dependent Component Analysis
63
12
Allan Kardec Barros
Introduction
63
1
Blind Source Separation by DCA
64
1
The ``Cyclone'' Algorithm
65
2
Experimental Results
67
1
Higher-Order Cyclostationary Signal Separation
68
1
Conclusion
68
2
Appendix: Proof of ACF Property 3
70
5
Part III Ensemble Learning and Applications
Ensemble Learning
75
18
Harri Lappalainen
James W. Miskin
Introduction
75
1
Posterior Averages in Action
76
2
Approximations of Posterior PDF
78
1
Ensemble Learning
79
4
Model Selection in Ensemble Learning
81
1
Connection to Coding
82
1
EM and MAP
83
1
Construction of Probabilistic Models
83
3
Priors and Hyperpriors
85
1
Examples
86
5
Fixed Form Q
86
2
Free Form Q
88
3
Conclusion
91
2
References
92
1
Bayesian Non-Linear Independent Component Analysis by Multi-Layer Perceptrons
93
30
Harri Lappalaien
Antti Honkela
Introduction
93
2
Choosing Among Competing Explanations
95
2
Non-Linear Factor Analysis
97
9
Definition of the Model
97
2
Cost Function
99
3
Update Rules
102
4
Non-Linear Independent Factor Analysis
106
1
Experiment
107
9
Learning Scheme
107
1
Helix
108
1
Non-Linear Artificial Data
109
6
Process Data
115
1
Comparison with Existing Methods
116
2
SOM and GTM
116
1
Auto-Associative MLPs
117
1
Generative Learning with MLPs
118
1
Conclusion
118
2
Validity of the Approximations
118
1
Initial Inversion by Auxiliary MLP
119
1
Future Directions
120
1
Acknowledgements
120
3
Ensemble Learning for Blind Image Separation and Deconvolution
123
22
James Miskin
David J. C. MacKay
Introduction
123
1
Separation of Images
124
10
Learning the Ensemble
126
3
Learning the Model
129
1
Example
129
3
Parts-Based Image Decomposition
132
2
Deconvolution of Images
134
6
Conclusion
140
1
Acknowledgements
141
4
References
141
4
Part IV Data Analysis and Applications
Multi-Class Independent Component Analysis (MUCICA) for Rank-Deficient Distributions
145
16
Francesco Palmieri
Alessandra Budillon
Introduction
145
1
The Rank-Deficient One Class Problem
146
5
Method I: Three Blocks
148
1
Method II: Two Blocks
149
1
Method III: One Block
150
1
The Rank-Deficient Multi-Class Problem
151
3
Simulations
154
4
Conclusion
158
3
References
159
2
Blind Separation of Noisy Image Mixtures
161
22
Lars Kai Hansen
Introduction
161
1
The Likelihood
162
1
Estimation of Sources of the Case of Known Parameters
163
1
Joint Estimation of Sources, Mixing Matrix, and Noise Level
164
2
Simulation Example
166
1
Generalization and the Bias-Variance Dilemma
167
3
Application to Neuroimaging
170
5
Conclusion
175
3
Acknowledgments
178
1
Appendix: The Generalized Boltzmann Learning Rule
179
4
Searching for Independence in Electromagnetic Brain Waves
183
18
Ricardo Vigario
Jaakko Sarela
Erkki Oja
Introduction
183
1
Independent Component Analysis
184
2
The Model
184
1
The FastICA Algorithm
184
2
Electro- and Magnetoencephalography
186
2
The Analysis of the Linear ICA Model
188
1
The Analysis of EEG and MEG Data
189
5
Artifact Identification and Removal from EEG/MEG
189
2
Analysis of Multimodal Evoked Fields
191
2
Segmenting Auditory Evoked Fields
193
1
Conclusion
194
7
ICA on Noisy Data: A Factor Analysis Approach
201
16
Shiro Ikeda
Introduction
201
1
Factor Analysis and ICA
202
3
Factor Analysis
202
2
Factor Analysis in Preprocessing
204
1
ICA as Determining the Rotation Matrix
204
1
Experiment with Synthesized Data
205
3
MEG Data Analysis
208
5
Experiment with Phantom Data
209
2
Experiment with Real Brain Data
211
2
Conclusion
213
2
Acknowledgments
215
2
Analysis of Optical Imaging Data Using Weak Models and ICA
217
18
John Porrill
James V. Stone
Jason Berwick
John Mayhew
Peter Coffey
Introduction
217
1
Linear Component Analysis
218
1
Singular Value Decomposition
219
2
SVD Applied to OI Data Set
220
1
Independent Component Analysis
221
4
Minimisation Routines
223
1
Application of SICA to OI Data
223
2
The Weak Causal Model
225
2
Weak Causal Model Applied to the OI Data Set
226
1
Some Remarks on Significant Testing
227
1
The Weak Periodic Model
227
1
Regularised Weak Models
228
1
Regularised Weak Causal Model Applied to OI Data
229
1
Image Goodness and Multiple Models
230
1
A Last Look at the OI Data Set
231
1
Conclusion
232
3
References
233
2
Independent Components in Text
235
22
Thomas Kolenda
Lars Kai Hansen
Sigurdur Sigurdsson
Introduction
235
3
Vector Space Representations
235
2
Latent Semantic Indexing
237
1
Independent Component Analysis
238
8
Noisy Separation of Linear Mixtures
239
3
Learning ICA Text Representations on the LSI Space
242
1
Document Classification Based on Independent Components
243
1
Keywords from Context Vectors
244
1
Generalisation and the Bias-Variance Dilemma
244
2
Examples
246
5
MED Data Set
248
1
CRAN Data Set
249
2
Conclusion
251
6
Seeking Independence Using Biological-Inspired ANN's
257
20
Pei Ling Lai
Darryl Charles
Colin Fyfe
Introduction
257
1
The Negative Feedback Network
258
1
Independence in Unions of Sources
259
5
Factor Analysis
261
1
Minimal Overcomplete Bases
261
3
Canonical Correlation Analysis
264
5
Extracting Multiple Correlations
266
1
Using Minimum Correlations to Extract Independent Sources
267
1
Experiments
268
1
ϵ-Insensitive Hebbian Learning
269
6
Is this a Hebbian Rule?
270
1
Extraction of Sinusoids
271
2
Noise Reduction
273
2
Conclusion
275
2
References
275
2
Index
277