A Strongly Consistent Sparse $k$-means Clustering with Direct $l_1$ Penalization on Variable Weights
This provides a non-parametric method for feature selection in clustering, addressing the challenge of high-dimensional data where features outnumber observations, though it appears incremental as it builds on existing k-means and lasso techniques.
The authors tackled the problem of sparse clustering in high-dimensional data by proposing the LW-k-means algorithm, which directly applies a lasso penalty to feature weights for feature selection, and they demonstrated its strong consistency and competitive performance in accuracy and computational time against state-of-the-art methods.
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.