SVD can be understood from a geometric sense for square matrices as a transformation on a vector. Consider a square n x n matrix M multiplying a vector v to produce an output vector w: w = M*v The singular value decomposition M is the product of three matrices M=U*S*V, so w=U*S*V*v. U and V … Read more
Sympy makes this straightforward. >>> from sympy import Matrix >>> A = [[2, 3, 5], [-4, 2, 3], [0, 0, 0]] >>> A = Matrix(A) >>> A * A.nullspace()[0] Matrix([ [0], [0], [0]]) >>> A.nullspace() [Matrix([ [-1/16], [-13/8], [ 1]])]
SVD is not used to normalize the data, but to get rid of redundant data, that is, for dimensionality reduction. For example, if you have two variables, one is humidity index and another one is probability of rain, then their correlation is so high, that the second one does not contribute with any additional information … Read more
Looking into the source via the link you provided, TruncatedSVD is basically a wrapper around sklearn.utils.extmath.randomized_svd; you can manually call this yourself like this: from sklearn.utils.extmath import randomized_svd U, Sigma, VT = randomized_svd(X, n_components=15, n_iter=5, random_state=None)
To decide how many eigenvalues/eigenvectors to keep, you should consider your reason for doing PCA in the first place. Are you doing it for reducing storage requirements, to reduce dimensionality for a classification algorithm, or for some other reason? If you don’t have any strict constraints, I recommend plotting the cumulative sum of eigenvalues (assuming … Read more
I was trying to figure this out as well, 2 years later. But I got my answers; hopefully it’ll help someone. You need 2 audio recordings. You can get audio examples from http://research.ics.aalto.fi/ica/cocktail/cocktail_en.cgi. reference for implementation is http://www.cs.nyu.edu/~roweis/kica.html ok, here’s code – [x1, Fs1] = audioread(‘mix1.wav’); [x2, Fs2] = audioread(‘mix2.wav’); xx = [x1, x2]’; yy … Read more