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Can someone help me on Sparse PCA? I am using the "elasticnet" package to perform sparse PCA. I am having a hard time in figuring out how many nonzero values should a component contain?

For example, In this code:

sparse.pca.result  <-  spca(X, K = 2, type = "predictor", sparse = "varnum", para = c(4, 4))

(para = c(4, 4)) indicates the number of non-zero components for each of the two PC’s respectively.

So the question is, how to identify the number of non-zero components?

I hope that someone could help me on this.

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  • $\begingroup$ Also, can someone please give me good sites or references about sparse PCA? Preferrably with examples and interpretations $\endgroup$ – Jonalyn Jul 27 '16 at 15:16
  • $\begingroup$ The reference is web.stanford.edu/~hastie/Papers/spc_jcgs.pdf , there are examples in section 5. $\endgroup$ – altroware Mar 24 '20 at 8:48
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One way to do this a little more adaptively is to specify the penalty instead of the number of nonzeroes you want. (Set sparse='penalty'.) Then you can specify the same parameter value across all components, while still allowing them to have different levels of sparsity.

Ordinarily, one might select the penalty parameter via cross-validation, but spca cannot deal with missing values, so it's hard to hold out a set of entries. You could hack together something similar, though:

  • Train the SPCA, holding out one case. You'll obtain L and R such that $X_{-1} \approx LR$. (Suppose $X_{-1}$ has cases as rows, and you left out row 1.)
  • Using half the variables (columns), fit a regression model to predict $X_{1}$ from $R$. You'll obtain $L_1$ such that $L_1R \approx X_{1}$.
  • Measure the predictive accuracy of the regression model using the other half of the variables.

You should probably hold out more than 1 row at a time.

I'll look for references if anybody's still looking at this page -- drop me a comment.

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  • $\begingroup$ I'm looking at this pages, and yes, can you please dig more references for this? $\endgroup$ – altroware Mar 24 '20 at 8:50
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    $\begingroup$ It seems to be standard practice in collaborative filtering, but I haven't found academic papers after a light search. This is also tricky and I think I may have screwed it up. I'll give it some thought and try to get back to you soon. $\endgroup$ – eric_kernfeld Mar 25 '20 at 21:07

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