臺灣博碩士論文加值系統

Network component analysis (NCA) and independent component analysis (ICA) both are the ways of redundancy reduction. These statistical methods are for transforming an observed multidimensional random vector into lowerdimension. In this thesis, we use two different algorithms for linear ICA: fast fixed-point algorithm and joint approximate diagonalization of eigenmatrices algorithm. We compare these three techniques that the ability of
reconstructing the hidden regulatory layers, via the simulation studies and a real data examples. We also investigate the sensitivity of the reconstructed signals to inaccuracies in the strength of network connectivity.

Network component analysis (NCA) and independent component analysis (ICA) both are the ways of redundancy reduction. These statistical methods are for transforming an observed multidimensional random vector into lowerdimension. In this thesis, we use two different algorithms for linear ICA: fast fixed-point algorithm and joint approximate diagonalization of eigenmatrices algorithm. We compare these three techniques that the ability of
reconstructing the hidden regulatory layers, via the simulation studies and a real data examples. We also investigate the sensitivity of the reconstructed signals to inaccuracies in the strength of network connectivity.

1 Introduction 1
2 Independent Component Analysis 2
2.1 Independent Component Analysis by Negentropy . . . . . . . 4
2.2 Independent Component Analysis by Kurtosis . . . . . . . . . 6
2.3 Fast Fixed-Point Algorithm . . . . . . . . . . . . . . . . . . . 8
2.3.1 The Algorithm for one unit . . . . . . . . . . . . . . . 8
2.3.2 The Algorithm for several units . . . . . . . . . . . . . 9
2.4 Joint Approximate Diagonalization of Eigen-matrices Algorithm 9
2.4.1 The Algorithm . . . . . . . . . . . . . . . . . . . . . . 10
3 Network Component Analysis 11
3.1 The Network Component Analysis Model . . . . . . . . . . . . 12
3.2 Criteria for NCA . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 The Algorithm of NCA . . . . . . . . . . . . . . . . . . . . . . 17
4 Examples 18
4.1 Synthetic Data of Two Sources . . . . . . . . . . . . . . . . . 18
4.2 Synthetic Data of Three Sources . . . . . . . . . . . . . . . . . 20
4.3 Real Data of Three Sources . . . . . . . . . . . . . . . . . . . 22
5 Conclusion 23

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