Abstract

A Sparse weighted consensus method for multi-view clustering
Authors: Ndèye Niang, Mouhamadou Lamine Ndao, Mory Ouattara
We are in the setting of multi-view clustering where observations are described by variables divided in several homogeneous and meaningful blocks. As the blocks are supposed to be homogeneous, preserving this block homogeneity would help to exhibit the underlying structure of the individuals. So, at a first level, the individuals are clustered according to each block separately and the resulting partitions (called contributory partitions) are aggregated in a consensual partition in a second step. Therefore, this multi-view clustering issue is reformulated as a consensus of partitions one. 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 to indicator matrices and association matrices whose entries are 1 if two individuals are in the same cluster and 0 otherwise. Using association matrices avoid the label switching issue. It has been pointed out by several authors, that simple consensus methods such as CSPA (Cluster based Similarity Partitioning Algorithm can yield unstable results when the contributory partitions are significantly different and if some of input partitions are highly correlated. This redundancy could bias the final partition towards these correlated partitions. To address these limitations, weighted consensus methods have been then proposed with methods such as WNMF. We propose a sparse weighted consensus method based on Constrained Singular Value Decomposition and the RV correlation coefficient between the association matrix to find an unique partition from contributory partitions. The results on simulated data as well as real ones show the relevance of the proposed method particularly when dealing with redundant partitions.