Patch Tensor-Based Multigraph Embedding Framework for Dimensionality Reduction of Hyperspectral Images

Graph-based dimensionality reduction (DR) techniques are of great interest in the field of image processing and especially on the analysis of hyperspectral images (HSIs). Considering the characteristics of hyperspectral data, many different types of graphs were designed to describe the structure of HSIs. Generally, the algorithms based on these graphs achieved promising performance. However, most of them only focus on how to improve the measurement of similarity between the data points by a single graph. Specifically, vector-based graph methods fail to capture the spatial information, while tensor-based graph methods assume that the pixels in each patch tensor belong to the same class, which is not exactly correct in practice. To overcome these shortcomings, this article proposes a patch tensor-based multigraph embedding (PTMGE) framework for the DR of HSIs, in which three different types of subgraphs are constructed to comprehensively describe the intrinsic geometrical structures of HSIs. First, a tensor subgraph is constructed to capture the spatial information and local geometrical structure. Second, for each two neighboring patch tensors in the tensor graph, a bipartite graph is designed to characterize the pixel-based relationships between the patch tensors. Then, considering that the diversity of pixels may be existed in each patch tensor, a pixel-based subgraph is built to describe the inner geometrical structures of every patch tensor. Finally, a novel graph fusion strategy is designed to calculate a final similarity matrix for projection learning. Experiments on three real hyperspectral data sets are conducted, and comparison with some state-of-the-art algorithms validated the effectiveness of our proposed PTMGE method.