Multi-view data representation via adaptive label propagation nonnegative matrix factorization

Nonnegative matrix factorization (NMF) integrating label propagation (LP) algorithm can enhance the discrimination ability of low-dimensional representations. However, traditional LP-based NMF approaches require the construction of a k-nearest neighbor graph in advance to obtain the weight matrix for LP. This increases the burden of adjusting the neighborhood parameter k and leads to a suboptimal weight matrix. To address these issues, an Adaptive Label Propagation NMF (ALPNMF) framework is designed by jointly minimizing the data reconstruction error and the predicted soft label reconstruction error. First, ALPNMF completes neighbor selection and weight calculation simultaneously, without adjusting the neighborhood parameter k. Second, ALPNMF takes into account the dependence between the graph weight learning and LP, thereby yielding the globally optimal graph weight matrix for LP and the more accurate predicted soft label matrix for guiding the decomposition process. Finally, with the aim of combining the information from diverse views to acquire more efficient low-dimensional representations, we extend ALPNMF to a new multi-view NMF approach named Multi-view data representation via Adaptive Label Propagation NMF (MALPNMF). Experimental results on five benchmark multi-view datasets demonstrate that MALPNMF outperforms other state-of-the-art multi-view NMF methods.