Density-Weighted Dissimilarity-Based Sparse Subset Selection Algorithm

The recently proposed Dissimilarity-Based Sparse Subset Selection (DS3) algorithm can select an informative subset from the original dataset to represent the data, thereby removing redundancy and irrelevance in datasets. However, the DS3 algorithm has two main limitations: (1) It is sensitive to the regularization parameter; (2) Despite the proposed strategy for handling outliers, the algorithm remains sensitive to outliers. To address these issues, a density-weighted DS3 (DWDS3) algorithm is proposed. DWDS3 utilizes the sample density information from the dissimilarity matrix, sums each row to generate weight factors, and applies weighting to the rows of the membership matrix. Through this weighting operation, the DWDS3 can enhance the robustness of the original algorithm to regularization parameters and outliers. DWDS3 can be solved using a weighted version of the soft-thresholding operator within the framework of the Alternating Direction Method of Multipliers (ADMM). Experimental results demonstrate that DWDS3 effectively reduces the sensitivity of the original algorithm to the regularization parameter and outliers.