Cluster structure augmented deep nonnegative matrix factorization with low-rank tensor learning

Clustering approaches based on deep nonnegative matrix factorization have received significant attention because it can learn hierarchical semantics from data in a layer-wise manner. However, latent representation learning and clustering are two separate processes in these models, leading to information loss and sub-optimal clusterings. Furthermore, if data contain complex structure or noise, the pre-defined graph in data space will not be precise enough for graph-regularized deep nonnegative matrix factorization models. Moreover, most of them maintain the similarity graph at the top layer, neglecting the information covered by other layers. In this paper, Cluster Structure Augmented Deep Nonnegative Matrix Factorization with Low-rank Tensor Learning is proposed. First, as representations at different layers cover different data abstractions, a learning mechanism is leveraged to generate multiple local similarity graphs based on representations from different layers, thus maintaining diversity across layers. Then, a low-rank third-order tensor is constructed by stacking these graphs to capture the high-order consistency across layers, thus capturing the intrinsic property of data. Third, clustering is integrated into the framework, allowing the cluster structure to facilitate multi-layer matrix factorization and graph structure learning, thereby generating discriminative representations. Experimental results on several datasets demonstrate that the proposed model outperforms several state-of-the-art methods.