Independent Components Analysis
目录Ambiguity
ICA is ambiguous to scaling and permutation. but usually it doesn't matter.
As long as the data is not Gaussian, it's possible, given enough data, to recover the n independent sources.
Densities and Linear Transformations
\[p_x(x)=p_s(Wx)\,|W| \]ICA
\[p(x)=\prod_{i=1}^n p_s(w_i^Tx)\,|W| \]s is source and x is the detection. and \(x=As=W^{-1}s\)
we assume the CDF of \(s\) is \(g(s)\) is sigmoid. the log likelihood is given by
\[\ell(W)=\sum_{i=1}^m(\sum_{j=1}^n \log g'(w_j^Tx^{(i)})+\log|W|) \]m training samples, and n independent sources of voice.
the stochastic gradient ascent process is:
\[W := W +\alpha([1-2g(w_1^T x^{(i)});...;1-2g(w_n^T x^{(i)})]x^{(i)^T}+(W^T)^{-1}) \] 标签：分析,independent,given,log,Tx,Independent,独立,sources,成分 From： https://www.cnblogs.com/BUAA-Stargazer/p/16626036.html