LapSDNMF: Label propagation assisted soft-constrained deep non-negative matrix factorisation for semi-supervised multi-view clustering

Semi-supervised methods based on non-negative matrix factorisation have emerged as a popular approach for clustering. However, the pressing challenge of capturing complex non-linear relationships within multi-view data is seldom considered in the semi-supervised context.This study introduces a fundamentally novel framework: Label Propagation Assisted Soft-constrained Deep Non-negative Matrix Factorisation for Semi-supervised Multi-view Clustering (LapSDNMF).LapSDNMF innovatively integrates deep hierarchical modelling with label propagation and soft constraint to jointly exploit the non-linear representation learning and extract accurate latent features from limited labelled data. By embedding a predictive membership matrix as a soft constraint, it enables similarly labelled samples to be projected into shared regions, better reflecting real-world data structures. The incorporation of graph-based regularisation within the deep architecture facilitates effective label propagation while preserving the manifold structure at each layer. LapSDNMF unifies deep learning and graph-theoretic techniques within a coherent optimisation framework. We also develop a novel, efficient algorithm based on multiplicative update rules to solve the resulting optimisation problem.LapSDNMF significantly outperforms state-of-the-art multi-view clustering methods across five diverse real-world datasets. Specifically, it achieves improvements in F-score of 10.2%, 7.2%, 8.8%, 1.4%, and 6.1% on the Yale, Reuters-MinMax, Caltech7, 3-Sources, and Caltech20 datasets, respectively, compared with the best-performing baseline method.