EPTAS for k-means Clustering of Affine Subspaces

Abstract

We consider a generalization of the fundamental k-means clustering for data with incomplete or corrupted entries. When data objects are represented by points in R^d, a data point is said to be incomplete when some of its entries are missing or unspecified. An incomplete data point with at most unspecified entries corresponds to an axis-parallel affine subspace of dimension at most , called a -point. Thus we seek a partition of n input -points into k clusters minimizing the k-means objective. For =0, when all coordinates of each point are specified, this is the usual k-means clustering. We give an algorithm that finds an (1+ )-approximate solution in time f(k,, ) n^2 d for some function f of k,, and only.

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