Parallel Processing and Applied Mathematics

We present a range of new incremental (single-pass streaming) algorithms for incremental principal components analysis (IPCA) and show that they are more effective than exiting ones. IPCA algorithms process the columns of a matrix A one at a time and attempt to build a basis for a low-dimensional subspace that spans the dominant subspace of A. We present a unified framework for IPCA algorithms, show that many existing ones are parameterizations of it, propose new sophisticated algorithms, and show that both the new algorithms and many existing ones can be implemented more efficiently than was previously known. We also show that many existing algorithms can fail even in easy cases and we show experimentally that our new algorithms outperform existing ones.

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