Deep graph regularized nonnegative Tucker decomposition for image data analysis

Nonnegative Tucker decomposition (NTD) is widely recognized as an effective tool for image analysis. However, the single-layer structure of the original NTD model is insufficient for capturing multiple directional representations and local manifold structural information from the raw image data. To overcome these limitations, we extend the single-layer framework to a deep graph regularized nonnegative Tucker decomposition (DGNTD) structure by harmoniously unifying deep learning and graph regularization terms in NTD. DGNTD constructs a hierarchical deep structure and decomposes image data into several layers that describe the interconnections of different layers throughout the deep structure. Furthermore, DGNTD with graph learning utilizes a graph structure to express the relationships between samples, which allows for the depiction of the inner geometrical relationships between samples while preserving computational feasibility. In addition, tests on three image datasets, including COIL20, ORL, and PIE, are used to assess the effectiveness of the proposed method.