Sparse possibilistic c-means clustering with Lasso. (June 2023) - Yang, Miin-Shen; Benjamin, Josephine B.M.
Highlights: Possibilistic c-means (PCM) clustering by incorporating the sparsity idea with feature weights is further studied. We propose two approaches that make the PCM clustering with the least absolute shrinkage and selection operator (Lasso), called S-PCM1 and S-PCM2. Synthetic and real data sets are used to compare the proposed S-PCM1 and S-PCM2 with some existing algorithms. Experimental results and comparisons demonstrate the good effectiveness and usefulness of the proposed S-PCM1 and S-PCM2 algorithms. Abstract: Krishnapuram and Keller first proposed possibilistic c-means (PCM) clustering in 1993. Afterward, PCM was widely studied with various extensions. The PCM algorithm and its extensions always treat feature components under equal importance, but, in real applications, different features may better have different weights. Recently, Yang and Benjamin in 2021 proposed a feature-weighted PCM clustering with feature reduction. Although Yang and Benjamin (2021) can reduce feature dimensions, it still encounters the curse of dimensionality for high dimensional data. One possible way to address this problem is to conduct a sparse clustering technique. In this paper, we further study the PCM clustering by incorporating the idea of sparsity with different feature weights. We propose two approaches that use the PCM clustering with the least absolute shrinkage and selection operator (Lasso). The first one is the sparse PCM subject to a Lasso constraint of feature weights, called S-PCM1. The second is the sparse PCM by adding a Lasso penalty term of feature weights in the objective function, called S-PCM2. We show that S-PCM1 and S-PCM2 are theoretically the same, and both can induce sparsity in features, but they use different procedures in algorithms. Synthetic and real data sets are used to compare S-PCM1 and S-PCM2 with some existing sparsity clustering algorithms. Experimental results and comparisons demonstrate the effectiveness and usefulness of the proposed S-PCM1 and S-PCM2 clustering algorithms.