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Second order accurate distributed eigenvector computation for extremely large matrices
TL;DR: It is shown that averaging eigenvectors of randomly subsampled matrices efficiently approximates the true eigenvctors of the original matrix under certain conditions on the incoherence of the spectral decomposition.
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Abstract: We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that averaging eigenvectors of randomly subsampled matrices efficiently approximates the true eigenvectors of the original matrix under certain conditions on the incoherence of the spectral decomposition. This incoherence assumption is typically milder than those made in matrix completion and allows eigenvectors to be sparse. We discuss applications to spectral methods in dimensionality reduction and information retrieval.
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On Spectral Clustering: Analysis and an algorithm
Andrew Y. Ng,Michael I. Jordan,Yair Weiss +2 more
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TL;DR: A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.
Exact Matrix Completion via Convex Optimization
TL;DR: It is proved that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries, and that objects other than signals and images can be perfectly reconstructed from very limited information.