Self-weighted low-rank representation for multivariate compositional data

Compositional data can effectively capture the relative information among different parts of a whole, which is frequently utilized in practical applications in recent years. Unfortunately, few works are yet available for clustering multivariate compositional data, due to the potential challenges created by the complex grouping structure and the existence of uninformative variables. In this paper, we propose a self-weighted low-rank representation (SWLRR) method to cluster multivariate compositional data. Specifically, a variable weighting strategy is introduced to learn appropriate weights for different compositional data variables, which can highlight the informative variables and resist the uninformative ones. Meanwhile, for the need of exploring the grouping structure, the global and local structures of data are simultaneously captured within the weighted data space, which is realized through generalizing the self-expressive property and adding a graph constraint term to multivariate compositional data, respectively. Moreover, the low-rank constraint is imposed on the representation for robustness. On this basis, we construct a unified optimization framework and present the solving algorithm by means of the alternating direction method of multipliers (ADMM). Experimental results on the synthetic and practical datasets show the advantages of the proposed clustering method compared with other competitors, and demonstrate the effectiveness of the proposed method to recognize the contributions of different compositional data variables to the clustering process.