def ica(data, k, c):
n = data.count()
# reduce dimensionality
comps, latent, scores = svd4(data, k, 0)
# whiten data
whtMat = real(dot(inv(diag(sqrt(latent))), comps))
unwhtMat = real(dot(transpose(comps), diag(sqrt(latent))))
wht = data.map(lambda x: dot(whtMat, x))
# do multiple independent component extraction
B = orth(random.randn(k, c))
Bold = zeros((k, c))
iterNum = 0
minAbsCos = 0
tol = 0.000001
iterMax = 1000
errVec = zeros(iterMax)
while (iterNum < iterMax) & ((1 - minAbsCos) > tol):
iterNum += 1
# update rule for pow3 nonlinearity (TODO: add other nonlins)
B = wht.map(lambda x: outer(x, dot(x, B) ** 3)).sum() / n - 3 * B
# orthognalize
B = dot(B, real(sqrtm(inv(dot(transpose(B), B)))))
# evaluate error
minAbsCos = min(abs(diag(dot(transpose(B), Bold))))
# store results
Bold = B
errVec[iterNum - 1] = 1 - minAbsCos
# get unmixing matrix
W = dot(transpose(B), whtMat)
# get components
sigs = data.map(lambda x: dot(W, x))
return W, sigs, whtMat, unwhtMat
def pca(data, k):
comps, latent, scores = svd4(data, k, 0)
return comps, latent, scores