Autoencoder based Nonnegative Matrix Factorization with Collaborative Consensus for incomplete multiview clustering

Abstract

Aim of multiview clustering (MVC) is to partition the data into clusters by exploiting comple- mentary information from multiple views. Conventional MVC approaches generally assume that all views are fully observed; however, this assumption is often not true in real-world scenarios where data incompleteness is inevitable. The performance of conventional MVC models degrades by such missing views. This limitation of MVC methods has motivated the development of incomplete multiview clustering (IMVC) methods. Existing IMVC methods are although promising still face challenges like robust latent representation, cross-view consen- sus and structure preservation under high missing ratios. To overcome this limitation, a novel Autoencoder based Nonnegative Matrix Factorization with Collaborative Consensus for incomplete multiview clustering (IMVC-AENMF) framework is proposed. The proposed method integrates three key components: First, an autoencoder-like factorization strategy that imposes encoder–decoder consistency to enhance the stability of latent representations. Second, a collaborative consensus learning mechanism that aligns view-specific latent spaces with a shared consensus representation, enabling effective cross-view knowledge transfer despite incom- pleteness. Third, a graph Laplacian regularization term that preserves the intrinsic manifold structure and ensures cluster smoothness. The unified objective function is inherently nonconvex, and an efficient alternating optimization algorithm with multiplicative update rules is derived to guarantee convergence to a local opti- mum. Extensive experiments on five commonly used datasets and one real-world financial dataset demonstrate that our framework not only achieves superior clustering performance compared to state-of-the-art incomplete MVC methods but also exhibits strong robustness against varying missing rates, thereby providing a powerful solution for practical multiview learning applications.