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arXiv · 1903.10039

A Strongly Consistent Sparse $k$-means Clustering with Direct $l_1$ Penalization on Variable Weights

Saptarshi Chakraborty·Swagatam Das
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Abstract

We propose the Lasso Weighted $k$-means ($LW$-$k$-means) algorithm as a simple yet efficient sparse clustering procedure for high-dimensional data where the number of features ($p$) can be much larger compared to the number of observations ($n$). In the $LW$-$k$-means algorithm, we introduce a lasso-based penalty term, directly on the feature weights to incorporate feature selection in the framework of sparse clustering. $LW$-$k$-means does not make any distributional assumption of the given dataset and thus, induces a non-parametric method for feature selection. We also analytically investigate the convergence of the underlying optimization procedure in $LW$-$k$-means and establish the strong consistency of our algorithm. $LW$-$k$-means is tested on several real-life and synthetic datasets and through detailed experimental analysis, we find that the performance of the method is highly competitive against some state-of-the-art procedures for clustering and feature selection, not only in terms of clustering accuracy but also with respect to computational time.

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Saptarshi Chakraborty, Swagatam Das. 2019-03-24. A Strongly Consistent Sparse $k$-means Clustering with Direct $l_1$ Penalization on Variable Weights. https://arxiv.org/abs/1903.10039

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