SPARSE k-MEANS WITH ℓ∞/ℓ0 PENALTY FOR HIGH-DIMENSIONAL DATA CLUSTERING

One of the existing sparse clustering approaches, ℓ1-k-means, maximizes the weighted between-cluster sum of squares subject to the ℓ1 penalty. In this paper, we propose a sparse clustering method based on an ℓ∞/ℓ0 penalty, which we call ℓ0-k-means. We design an efficient iterative algorithm for solv...

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Bibliographic Details
Published inStatistica Sinica Vol. 28; no. 3; pp. 1265 - 1284
Main Authors Chang, Xiangyu, Wang, Yu, Li, Rongjian, Xu, Zongben
Format Journal Article
LanguageEnglish
Published Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association 01.07.2018
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ISSN1017-0405
1996-8507

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Summary:One of the existing sparse clustering approaches, ℓ1-k-means, maximizes the weighted between-cluster sum of squares subject to the ℓ1 penalty. In this paper, we propose a sparse clustering method based on an ℓ∞/ℓ0 penalty, which we call ℓ0-k-means. We design an efficient iterative algorithm for solving it. To compare the theoretical properties of ℓ1 and ℓ0-k-means, we show that they can be explained explicitly from a thresholding perspective based on different thresholding functions. Moreover, ℓ1 and ℓ0-k-means are proven to have a screening consistent property under Gaussian mixture models. Experiments on synthetic as well as real data justify the outperforming results of ℓ0 with respect to ℓ1-k-means.
ISSN:1017-0405
1996-8507