臺灣博碩士論文加值系統

In this thesis, two algorithms Fast ICA and Jade ICA, in independent component
analysis are performed to find the actual sources from the mixing
sources. It is well-known that the actual sources must be mutually independent
in ICA methods and be far away from the Gaussian distribution.
A new method called network component analysis (NCA) can also be applied
to blind sources cases without the mutually independence of sources
assumption. To illustrate the applications of these approaches, some simulation
studies and a real data example are provided in this thesis.

In this thesis, two algorithms Fast ICA and Jade ICA, in independent component
analysis are performed to find the actual sources from the mixing
sources. It is well-known that the actual sources must be mutually independent
in ICA methods and be far away from the Gaussian distribution.
A new method called network component analysis (NCA) can also be applied
to blind sources cases without the mutually independence of sources
assumption. To illustrate the applications of these approaches, some simulation
studies and a real data example are provided in this thesis.

1 Introduction 1
2 Independent Component Analysis 2
2.1 Independent Component Analysis Model . . . . . . . . . . . . 3
2.2 Fast ICA by a fixed-point algorithm . . . . . . . . . . . . . . . 4
2.2.1 Whitening . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 Measuring non-Gaussianity . . . . . . . . . . . . . . . 4
2.2.3 Approximates of the negentropy . . . . . . . . . . . . . 6
2.2.4 The FastICA algorithm . . . . . . . . . . . . . . . . . . 7
2.3 Joint Approximate Diagonalization of Eigen-matrices Independent
Component Analysis . . . . . . . . . . . . . . . . . . 8
2.3.1 Cumulant based method and Algebraic structure . . . 8
2.3.2 Cumulant matrix and joint diagonality criterion . . . . 9
2.3.3 The Jade ICA algorithm . . . . . . . . . . . . . . . . . 10
3 Network Component Analysis 12
3.1 Network Component Analysis Model . . . . . . . . . . . . . . 13
3.2 Criteria for NCA . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Method for NCA . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Simulation 15
4.1 Simulation I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Simulation II . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Simulation III . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Real Data Analysis 21
5.1 Spectral Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
6 Conclusion 25
Simulation result graph 26
References 39
Appendix 40

James. C. Liao et al ., Network component analysis: Reconstruction of regulatory
signals in biological systems, PNAS, vol. 100, no. 26, 15522-15527,
2003.
James. C. Liao et al ., A generalized framework for Network Component
Analysis, PNAS, vol. 2, no. 4, 289-300, 2005.
Jean-Fran¸cois Cardoso, and Antoine Souloumiac, Blind beamforming for non
Gaussian signals, IEE-Proceedings-F, vol. 140, no. 6, 362-370, 1993.
Jean-Fran¸cois Cardoso, High-Order Contrasts for Independent Component
Analysis, Neural Computation 11, 157-192, 1999.
Stephen Roberts, and Richard Everson (2001), Independent Component Analysis:
Principles and Practice.
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