Consistency of Sparse PCA in High Dimension, Low Sample Size Contexts

Details Consistency of Sparse PCA in High Dimension, Low Sample Size Contexts Consistency of Sparse PCA in High Dimension, Low Sample Size Contexts

2011-04-21

arxiv.org/abs/1104.4289v1

Mathematics

Statistics Theory

Scientific paper

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension, Low Sample Size (HDLSS)). Under the previously studied spike covariance assumption, we show that Sparse PCA remains consistent under the same large spike condition that was previously established for conventional PCA. Under a broad range of small spike conditions, we find a large set of sparsity assumptions where Sparse PCA is consistent, but PCA is strongly inconsistent. The boundaries of the consistent region are clarified using an oracle result.

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