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- W1569180792 abstract "Traditionally, clustering problems are investigated under the assumption that all objects must be clustered. A shortcoming of this formulation is that a few distant objects, called outliers, may exert a disproportionately strong influence over the solution. In this work we investigate the k-min-sum clustering problem while addressing outliers in a meaningful way.Given a complete graph G = (V,E), a weight function w : E →IN0 on its edges, and $p rightarrow {it {IN}_{o}}$ a penalty function on its nodes, the penalized k-min-sum problem is the problem of finding a partition of V to k+1 sets, {S1,...,Sk+1}, minimizing $sum_{i=1}^{k}$w(Si)+p(Sk+1), where for S⊆Vw(S) = $sum_{e={{it i},{it j}} subset {it S}}$we, and p(S) = $sum_{i in S}{^p_i}$.We offer an efficient 2-approximation to the penalized 1-min-sum problem using a primal-dual algorithm. We prove that the penalized 1-min-sum problem is NP-hard even if w is a metric and present a randomized approximation scheme for it. For the metric penalized k-min-sum problem we offer a 2-approximation." @default.
- W1569180792 created "2016-06-24" @default.
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- W1569180792 date "2005-01-01" @default.
- W1569180792 modified "2023-09-25" @default.
- W1569180792 title "Min Sum Clustering with Penalties" @default.
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- W1569180792 doi "https://doi.org/10.1007/11561071_17" @default.
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