Preprocessing Data

It is easier to estimate W if the measured signals have a mean of zero, a variance of one and zero correlation. The data is preprocessed to meet these goals before W is estimated.

Centering is achieved simply by subtracting the mean of signal from each reading of that signal.

A covariance matrix can be formed by taking the covariance between every pair of signals and forming a matrix. The covariance matrix will be square and symmetric. We can perform an eigenvalue decomposition on the covariance matrix and then transform the data so the covariance matrix of the transformed data is equal to the identity. This procedure is also called sphereing since it normalizes the eigenvalues of the covariance matrix.

C = VLVT

x = V L-1/2 VTx

After whitening we will have a new mixing matrix to find. The original mixing can be recovered by applying the inverse of the whitening operation on the new mixing matrix.

x = (V L-1/2 VT A)s = AS

However, now the new mixing matrix A is orthogonal. This puts another restraint on the system and further reduces the space in which we need to search for A. Similarly, since W=AT, the search space for W is reduced.


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