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