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

## TL;DR

This paper introduces MIMA, a novel semi-supervised data fusion method combining SSMA and MAPPER topological analysis, to improve land cover and climate zone classification using optical and polarimetric SAR data.

## Contribution

It is the first application of SSMA to fuse optical and SAR data and the first use of TDA in remote sensing, enhancing semi-supervised multi-sensor data fusion.

## Key findings

- MIMA outperforms traditional methods in classification accuracy.
- The method effectively leverages unlabeled data for improved fusion.
- Experimental results demonstrate superior performance in land cover and climate zone classification.

## Abstract

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 SAR data, which are multi-sensory data sources. Furthermore, we propose a MAPPER-induced manifold alignment (MIMA) for 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 our best 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. Experiment results on data fusion with respect to land cover land use classification and local climate zone classification suggest superior performance of MIMA.