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Use SVD for PCA and fix when channels > observations #3

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Use SVD for PCA and fix when channels > observations #3

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41 changes: 14 additions & 27 deletions ica/ica.py
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Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@
from numpy import dot
from numpy.linalg import matrix_rank, inv
from numpy.random import permutation
from scipy.linalg import eigh
from scipy.linalg import svd
from scipy.linalg import norm as mnorm

# Global constants
Expand Down Expand Up @@ -40,15 +40,6 @@ def fit(self, x2d):
return self


def diagsqrts(w):
"""
Returns direct and inverse square root normalization matrices
"""
Di = np.diag(1. / (np.sqrt(w) + np.finfo(float).eps))
D = np.diag(np.sqrt(w))
return D, Di


def pca_whiten(x2d, n_comp, verbose=True):
""" data Whitening
*Input
Expand All @@ -59,23 +50,19 @@ def pca_whiten(x2d, n_comp, verbose=True):
white : whitening matrix (Xwhite = np.dot(white,X))
dewhite : dewhitening matrix (X = np.dot(dewhite,Xwhite))
"""
x2d_demean = x2d - x2d.mean(axis=1).reshape((-1, 1))
NSUB, NVOX = x2d_demean.shape
if NSUB > NVOX:
cov = dot(x2d_demean.T, x2d_demean) / (NSUB - 1)
w, v = eigh(cov, eigvals=(NVOX - n_comp, NVOX - 1))
D, Di = diagsqrts(w)
u = dot(dot(x2d_demean, v), Di)
x_white = v.T
white = dot(Di, u.T)
dewhite = dot(u, D)
else:
cov = dot(x2d_demean, x2d_demean.T) / (NVOX - 1)
w, u = eigh(cov, eigvals=(NSUB - n_comp, NSUB - 1))
D, Di = diagsqrts(w)
white = dot(Di, u.T)
x_white = dot(white, x2d_demean)
dewhite = dot(u, D)
x2d_demean = x2d - x2d.mean(axis=1, keepdims=True)
NVOX = x2d_demean.shape[1]

u, s, _ = svd(x2d_demean)
u = u[:,:n_comp]
s = s[:n_comp] / np.sqrt(NVOX - 1)

D = np.diag(s)
Di = np.diag(1. / (s + np.finfo(float).eps))

white = dot(Di, u.T)
x_white = dot(white, x2d_demean)
dewhite = dot(u, D)
return (x_white, white, dewhite)


Expand Down