Graph Convolutional Optimal Transport for Hyperspectral Image Spectral Clustering

Abstract

Suffering from rich spectral and spatial information, the hyperspectral images (HSIs) that embed low-dimensional nonlinear manifolds lead to a challenging clustering task. In this article, we propose a promising clustering method for HSIs, termed as graph convolutional optimal transport (GCOT). For capturing the intrinsic geometric structure of data, we develop optimal transport (OT) on their graph embeddings. The OT problem learns discrete transport coupling to form a natural affinity matrix used for spectral clustering. Different from most other methods of building a graph with the Euclidean distance among neighborhoods, we leverage the OT probability to seek the edges of the graph that characterizes the local nonlinear structure of the original feature. For profound understanding of the proposed model, we prove the coupling holds sparsity and low-rank property that are beneficial to spectral clustering and provide its relationship with subspace clustering. To the best of our knowledge, this work could be one of the first spectral clustering methods using the OT theory. Several experiments on three widely used datasets with subjective and objective evaluation show that the proposed method dramatically outperforms the common existing methods and yields a comparable result with the state-of-the-art methods. Especially, it is significantly superior to the latter ones on computational efficiency.

Topics & Concepts