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Sparse PCA provides a linear combination of small number of features thatmaximizes variance across data. Although Sparse PCA has apparent advantagescompared to PCA, such as better interpretability, it is generally thought to becomputationally much more expensive. In this paper, we demonstrate thesurprising fact that sparse PCA can be easier than PCA in practice, and that itcan be reliably applied to very large data sets. This comes from a rigorousfeature elimination pre-processing result, coupled with the favorable fact thatfeatures in real-life data typically have exponentially decreasing variances,which allows for many features to be eliminated. We introduce a fast blockcoordinate ascent algorithm with much better computational complexity than theexisting first-order ones. We provide experimental results obtained on textcorpora involving millions of documents and hundreds of thousands of features.These results illustrate how Sparse PCA can help organize a large corpus oftext data in a user-interpretable way, providing an attractive alternativeapproach to topic models.

Large-Scale Sparse Principal Component Analysis with Application to Text Data