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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1Little remark : Principle $\rightarrow$ Principal – Jean Marie Sep 20 '16 at 10:38
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Full PCA means computing all the eigenvectors of the autocorrelation matrix $X X^T$ (where the points are the rows of $X$) and what you call the minor components correspond to the eigenvectors associated with the smallest eigenvalues, while the principal components are those associated with the highest eigenvalues.. – reuns Sep 20 '16 at 11:18
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So my question is if MCA is related to the eigenvectors corresponding to smallest eigenvalues of the autocorrelation matrix, then can we also compute them by a doing a full PCA and sorting the smallest components? – Bob Sep 20 '16 at 11:45
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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!
Bob
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