Sparse Weighted Multi-view Clustering
N. Niang${}^a$, M. L. Ndao${}^a$ and M. Ouattara${}^b$
${}^a$Conservatoire National des Arts et Métiers CNAM, Paris ${}^b$Université San Pédro, Côte d’Ivoire
We address multi-view clustering in which individuals are described by variables that are partitioned into several homogeneous and meaningful blocks. As the blocks are intended to be homogeneous, preserving this block homogeneity would help reveal the underlying structure of the individuals. So at a first level, the individuals are clustered according to each block separately, and the resulting partitions (contributory partitions) are aggregated in a consensual partition in a second step Niang and Ouattara [2019]. Therefore, this multi-view clustering issue is reformulated as a consensus of partitions problem. The choice of the first step clustering method is not addressed here. We only focus on the aggregation of the obtained partitions. These partitions are seen as categorical variables and then associated with indicator matrices and connectivity matrices whose entries are 1 if two individuals are in the same cluster and 0 if not. Using connectivity matrices avoids the label switching issue. It has been pointed out that simple consensus methods, such as CSPA (Cluster based Similarity Partitioning Algorithm) Strehl and Ghosh [2002], can yield unstable results when the contributory partitions are significantly different and if some of them are highly correlated.This redundancy could bias the final partition towards these correlated partitions. To address these limitations, weighted consensus methods have then been proposed with methods such as Weighted Non Matrix Factorization (WNMF) Li and Ding [2008]. We propose a sparse weighted consensus method based on Constrained Singular Value Decomposition Guillemot et al. [2019] and the RV correlation coefficient Robert and Escoufier [1976] between the connectivity matrices to find an unique partition from contributory ones. The results on simulated data as well as real ones show the relevance of the proposed method particularly when dealing with redundant partitions. In addition, the RV-based STATIS Lavit et al. [1994] method allows visualisation of the multi-view data as well as the clustering results.

Keywords: Sparsity ; Multi-view Clustering ; RV Coefficient