A Topological Data Analysis approach for retrieving Local Climate Zones patterns in satellite data

Abstract

In the context of geospatial studies, meaningful information may be hidden in the aspects of form and connectivity inscribed in the measurements. Therefore, here is proposed the use of H0 Persistent Homology (PH), a Topological Data Analysis tool to automatically summarize and quantify relevant spatial features in satellite data. With that aim, we extend the algebraic concepts of cubical complexes to the satellite data perspective and describe homology groups portrayal. As a proof by example, we present an inter-site comparison of Enhanced Vegetation Index from MODerate-resolution Imaging Spectroradiometer over fifteen regions worldwide. There, the Local Climate Zone (LCZ) framework is used to examine the outcomes of the PH filtration. Then, the features from every region that were encapsulated by the PH were compared against each other with the aid of the Bottleneck Distance metric. After that, it was performed a dimensionality reduction with a multi-dimensional scaling to build a 2-D geometry of the level of similarity among them. Thereby, the common aspects of the regions became explicit by their coordinates’ proximity in space. Then, with the use of the K-means algorithm, we were able to cluster those areas belonging to the same LCZ class. The results indicate that the proposed methods are robust to missing data in the satellite data and insensitive to a certain level of inhomogeneity in the spatial subsetting of data. Furthermore, the outcomes provide insights on several viable applications for future research.

Keywords

• Persistent homology
• Local climate zone
• EVI
• Bottleneck distance