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- W2266908258 abstract "We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and $dgeq n$. E.g., adjacency matrix of a graph, web-links, social network, document-terms, or image-features matrices. Our streaming algorithm stores at most $log ncdot k^{O(1)}$ input points in memory. If the stream is distributed among $M$ machines, the running time reduces by a factor of $M$, while communicating a total of $Mcdot k^{O(1)}$ (sparse) input points between the machines. % Our main technical result is a deterministic algorithm for computing a sparse $(k,epsilon)$-coreset, which is a weighted subset of $k^{O(1)}$ input points that approximates the sum of squared distances from the $n$ input points to every $k$ centers, up to $(1pmepsilon)$ factor, for any given constant $epsilon>0$. This is the first such coreset of size independent of both $d$ and $n$. Existing algorithms use coresets of size at least polynomial in $d$, or project the input points on a subspace which diminishes their sparsity, thus require memory and communication $Omega(d)=Omega(n)$ even for $k=2$. Experimental results real public datasets shows that our algorithm boost the performance of such given heuristics even in the off-line setting. Open code is provided for reproducibility." @default.
- W2266908258 created "2016-06-24" @default.
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- W2266908258 date "2015-11-29" @default.
- W2266908258 modified "2023-10-05" @default.
- W2266908258 title "k-Means for Streaming and Distributed Big Sparse Data" @default.
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- W2266908258 doi "https://doi.org/10.48550/arxiv.1511.08990" @default.
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