Dongmei Zhang

TL;DR: This paper mainly study seeding algorithms for spherical k-means clustering, for its special case (with separable sets), as well as for its generalized problem ($$\alpha $$α-spherical k- means clustered).

TL;DR: This paper presents four streaming algorithms for this problem by utilizing the concept of diminishing-return ratio, and analyzes these algorithms to obtain the corresponding approximation ratios, which generalize the previous results for the submodular case.

TL;DR: A local search for the k-means problem with (nonuniform) penalties (k-MPWP) is offered and the above approximation ratio is improved by using multi-swap operation and the sum of penalty cost for each client in P is minimized.

TL;DR: This paper proposes that the accuracy only involves the ratio of the maximal penalty value to the minimal one for the k-means problem when the penalty is uniform, and generalizes the k.means++ for k-Means problem to the penalty version.

TL;DR: It is proved that when against spherical k-means clustering with penalties but on separable instances, the algorithm is with an approximation ratio $$2\max \{3,M+1\}$$ with high probability, where M is the ratio of the maximal and the minimal penalty cost of the given data set.