SVD: Selected References
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Thresholded Correlation Matrix more easily computed with SVD
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“A Tutorial on Principal Component Analysis”, Jonathon Shlens
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Mathematical Facts about SVD (with view to Signal Processing) by S. J. Orfanidis
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“Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions”, Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp. A nice approach showing how to scale SVD to really large datasets.
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Blog on benchmarking sparse vs. dense SVD in scipy (Dense SVD is faster but takes more memory and is not applicable to large sparse matrices)
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Computation of the Singular Value Decomposition using Mesh-Connected Processors by Brent, Luk, Loan (an old paper showing a number of algorithms for SVD)
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Versatality of Singular Value Decomposition by Ravi Kannan ( backup link)
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Topic Modeling: A Provable Spectral Method by Ravi Kannan (Topic Modeling: A Provable Algorithm)
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Clustering: Does theory help? by Ravi Kannan (backup link to slides)
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Theory and Big Data by Ravi Kannan (how to apply provably fit a mixture of k Gaussians with the SVD)
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Low Rank Approximation and Regression in Input Sparsity Time by Kenneth L. Clarkson and David P. Woodruff (Nearly best rank k approx to A can be found in time linear in the number of non-zero entries in A)
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Simple and Deterministic Matrix Sketching by Edo Liberty (essentially running an algorithm for online SVD with small memory; very simple to implement but requires computing the SVD on a small matrix a large number of times.)