SPECTRAL CLUSTERING OF SPATIOTEMPORAL DATASETS

Abstract

The aim of this project is to use the spectral clustering algorithm to detect important geological and climate features by utilizing the properties of the graph Laplacian. Spectral clustering uses similarity measures between data points to construct the graph Laplacian and then finds clusters using the eigenvectors corresponding to its largest eigenvalues. Our work has found the relationships between connectivity parameters that are used to define pairwise similarity values between data points and the eigenvalues of the graph Laplacian. These relationships are then used to cluster spatiotemporal datasets, including some high-dimensional datasets. We have also tried to account for the phase differences that exist between two otherwise similar high-dimensional time series by using Dynamic Time Warping (DTW) and Uniform Manifold Approximation and Projection (UMAP). The relationships we find between the connectivity parameters and the graph Laplacian’s eigenvalues can be used to study eigengaps, which are important to perform cluster analysis and detect the number of clusters that can possibly be obtained without having an estimate beforehand.