Sparse Higher-Order Principal Components Analysis

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Sparse Higher-Order Principal Components Analysis
Traditional tensor decompositions such as the CANDECOMP / PARAFAC (CP) and Tucker decompositions yield higher-order principal components that have been used to understand tensor data in areas such as neuroimaging, microscopy, chemometrics, and remote sensing. Sparsity in high-dimensional matrix factorizations and principal components has been well-studied exhibiting many benefits; less attention has been given to sparsity in tensor decompositions. We propose two novel tensor decompositions that incorporate sparsity: the Sparse Higher-Order SVD and the Sparse CP Decomposition. The latter solves an 1-norm penalized relaxation of the single-factor CP optimization problem, thereby automatically selecting relevant features for each tensor factor. Through experiments and a scientific data analysis example, we demonstrate the utility of our methods for dimension reduction, feature selection, signal recovery, and exploratory data analysis of high-dimensional tensors.
Genevera Allen
Added 27 Sep 2012
Updated 27 Sep 2012
Type Journal
Year 2012
Where JMLR
Authors Genevera Allen
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