Optimal Neighborhood Kernel approach towards Incomplete Multi-View Clustering (OK-IMVC)

Abstract

Incomplete multi-view clustering (IMVC) has become one of the most prominent area of research in the recent past. The objective of IMVC is to integrate a set of pre-specified incomplete views in order to improve clustering performance. Among various excellent solutions already proposed in literature, multiple kernel k-means with incomplete kernels (MKKM-IK) [1] has been one of the benchmark research works, which formulates the incomplete multi-view clustering problem as a joint optimization problem framework whereby the imputation and clustering paradigms are integrated effortlessly. Both the processes are performed alternately in an iterative fashion to make used of the advantages of clustering in the subsequent imputation process and vice-versa. However, the computationally intensive and associated storage requirements demanded more efficient methods to be devised. These include the incomplete multi-view clustering with late fusion and the efficient and effective way proposed by Liu et al [2]. However, all of the above mentioned algorithms initialize the consensus clustering matrix, considering the unified kernel as a strict convex combination of the incomplete base kernels. This bold assumption suppresses the selectivity and representation capability of the unified kernel. In order to find a solution to the above problem, we propose a novel method called Optimal Neighborhood Kernel approach towards Incomplete Multi-View Clustering (OK-IMVC) which takes into account the representability of the unified or the optimal kernel. The consensus clustering matrix is continually updated via kernel k-means on the optimal neighborhood kernel, which is in turn computed based on the clustering results at the previous iteration. Specifically, our algorithm jointly learns a consensus clustering matrix, imputes each incomplete base matrix,learns the optimal neighborhood kernel and optimizes the corresponding alignment matrices. Further, we conduct comprehensive experiments to study the proposed OK-IMVC in terms of Normalized Mutual Information (NMI) index, purity score and running time. As indicated, our proposed method significantly and consistently outperforms some of the state-of-the-art algorithms with much less running time and memory.