Stochastic Subsampling for Factorizing Huge Matrices

Abstract

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm streams matrix columns while subsampling them to iteratively learn the matrix factors. At each iteration, the row dimension of a new sample is reduced by subsampling, resulting in lower time complexity compared to a simple streaming algorithm. Our method comes with convergence guarantees to reach a stationary point of the matrix-factorization problem. We demonstrate its efficiency on massive functional Magnetic Resonance Imaging data (2 TB), and on patches extracted from hyperspectral images (103 GB). For both problems, which involve different penalties on rows and columns, we obtain significant speed-ups compared to state-of-the-art algorithms.

IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, A Paraître

References in corpus (3)

• Pathwise coordinate optimization
• Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors
• Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares

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