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I am trying to understand step by step how correspondence analysis work. Suppose AxB (row x column) frequency matrix, roughly you should:

1) Calculate row and column profiles

2) Calculate chi-squared distances between rows and between columns

3) eigenvalues and eigenvectors from distance matrix

4) Inertia and chi-squared contribution

5) Biplot

6) Result analysis

My question is: are the distances from the row-row and column-column calculations merged into one matrix for eigenvalues and eigenvectors? What happens between chi-squared distance calculations and the actual base transformation?

Matias Andina
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  • I've explained (every necessary point, if to read carefully) correspondence analysis up to the biplot coordinates [here](http://stats.stackexchange.com/q/141754/3277). CA approximates chi-square distances on the plot (like PCA approximates euclidean distances) but it needs not compute those distances explicitly. Rather, it processes the frequency matrix directly, first making special normalization of it and then performing SVD. – ttnphns Nov 10 '15 at 17:23
  • I have seen your answer before...my algebra is not so good so I couldn't understand it, but I guess I can deal with the fact that both eigenvalues and vectors come from a single matrix and not two of them – Matias Andina Nov 10 '15 at 17:35
  • If you will have difficulty understanding step-by step computations in my answer please let me know and I will post an answer here showing all the computations, - tomorrow or the next day, when I have time. Cheers. – ttnphns Nov 10 '15 at 17:41
  • Don't worry, I'll give it a try later with the help of a linear algebra book I've used before (It'll help me get back in touch with those concepts also). My main issue with CA was with the matrix split and then only two (example) axis instead of four (two by split matrix). – Matias Andina Nov 10 '15 at 18:10

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