Why can't we use PCA to calculate MCA?

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I like to know what is the key difference between Minor component analysis (MCA) and principal component analysis (PCA) that there is a different algorithms in the literature for computing MCA, but one might say why not calculating principal components and sort them out in descending mode to get MCAs?

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Apparently the the way we usually calculate the eigenvectors of the autocorrelation matrix will not be numerically reliable when we do it for smallest eigenvalues of the matrix, and it is not important as in most of the cases they will be neglected! But for MCA the focus is on those eigenvectors so there is required a method to provide accurate numerical estimation of them!