大数据的快速投影聚类近似
Faster Projective Clustering Approximation of Big Data
摘要：
在投影聚类中，给定$R^d$中的一个n点集，根据给定的距离函数，将它们聚类到$R^d$中的$k$线性子空间的集合$S$中。这个问题的$\eps$ -coreset是输入点的加权（缩放）子集，使得对于每个这样的可能$S$，这些距离的总和近似为$(1+\eps)$的因子。我们建议，以减少现有的coreset的大小，建议第一$O(\log(m))$近似的情况下，$m$线聚类在$O(ndm)$时间，相比现有的$\exp(m)$解决方案。然后，我们在这些线上的项目点，并证明，对于一个足够大的$m$，我们得到一个投影聚类的核心集。我们的算法也推广到处理离群值。实验结果和开放的代码也提供。
英文摘要：
In projective clustering we are given a set of n points in $R^d$ and wish to cluster them to a set $S$ of $k$ linear subspaces in $R^d$ according to some given distance function. An $\eps$-coreset for this problem is a weighted (scaled) subset of the input points such that for every such possible $S$ the sum of these distances is approximated up to a factor of $(1+\eps)$. We suggest to reduce the size of existing coresets by suggesting the first $O(\log(m))$ approximation for the case of $m$ lines clustering in $O(ndm)$ time, compared to the existing $\exp(m)$ solution. We then project the points on these lines and prove that for a sufficiently large $m$ we obtain a coreset for projective clustering. Our algorithm also generalize to handle outliers. Experimental results and open code are also provided.
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