A Topological Data Analysis Guided Fusion Algorithm: Mapper-Regularized Manifold Alignment

Hyperspectral images and polarimetric synthetic aperture radar (PolSAR) data are two important data sources, yet they barely appear under the same scope, even though multi-modal data fusion is attracting more and more attention. To our best knowledge, this paper investigates for the first time semi-supervised manifold alignment (SSMA) for the fusion of the hyperspectral image and PolSAR data. The SSMA searches a latent space where different data sources are aligned, which is accomplished by using the label information and the topological structure of the data. This paper is the first attempt to apply topological data analysis (TDA), a recent mathematic sub-field of data analysis, in remote sensing. It aims to reveal relevant information from the shape of a data in its feature space, and has been proven powerful in medicine. The paper also proposes a novel algorithm, MAPPER-regularized manifold alignment, which embeds the TDA into a semi-supervised manifold alignment for the fusion of the hyper-spectral image and PolSAR data. The proposed algorithm exhibits superior performance in fusing a simulated EnMAP data set and a Sentinel-1 data set for an image of Berlin.