PCA for three dimensional features (or for 3 matrices)

Question

[pbio]

Hi All,

PCA for 3 dimensional matrices, I have 3 matrices (A (contains drugs), B(contains diseases), and C(contains Pathways)). Out of which Matrix A has 86 columns, matrix B has 177 columns and Matrix C has 877 columns(or features). Now I want to do some kind of feature selection using PCA which can reduce the features of C in combination with matrix A and B.

Can someone suggest me some ideas to perform such analyses? I have the PCA algorithm, but I actually want to understand how can I input such matrices to get the potential features from C affecting combination of A and B.

Thanks,

[Devon Ryan]

PCA only really makes sense on a single matrix. I assume you have the same number of rows for all of these matrices, so you could just merge them all together into a larger matrix and run the PCA on that. Personally I'd use something more traditional for feature selection like a random forest.

[pbio]

Exactly... this is what I was thinking.. thanks...

Answer 1

[Jean-Karim Heriche]

If you need to factorize N-way data then you should look into tensor factorization approaches. With more than 2 dimensions, things get a little bit more complicated and there are different factorization models to choose from. The equivalent of PCA is called PARAFAC or canonical polyadic decomposition (CANDECOMP). You'll find an introduction here. Depending on what you're trying to achieve and the nature of your data, there are a number of other factorizations to choose from.

Here is a very good review on tensor factorization.

[pbio]

Thanks Jean..