MIMA: MAPPER-Induced Manifold Alignment for Semi-Supervised Fusion of Optical Image and Polarimetric SAR Data

Multi-modal data fusion has recently been shown promise in classification tasks in remote sensing. Optical data and radar data, two important yet intrinsically different data sources, are attracting more and more attention for potential data fusion. It is already widely known that a machine learning-based methodology often yields excellent performance. However, the methodology relies on a large training set, which is very expensive to achieve in remote sensing. The semi-supervised manifold alignment (SSMA), a multi-modal data fusion algorithm, has been designed to amplify the impact of an existing training set by linking labeled data to unlabeled data via unsupervised techniques. In this paper, we explore the potential of SSMA in fusing optical data and polarimetric synthetic aperture radar (SAR) data, which are multi-sensory data sources. Furthermore, we propose a MAPPER-induced manifold alignment (MIMA) for the semi-supervised fusion of multi-sensory data sources. Our proposed method unites SSMA with MAPPER, which is developed from the emerging topological data analysis (TDA) field. To the best of our knowledge, this is the first time that SSMA has been applied on fusing optical data and SAR data, and also the first time that TDA has been applied in remote sensing. The conventional SSMA derives a topological structure using $k$-nearest neighbor (kNN), while MIMA employs MAPPER, which considers the field knowledge and derives a novel topological structure through the spectral clustering in a data-driven fashion. The experimental results on data fusion with respect to land cover land use classification and local climate zone classification suggest superior performance of MIMA.