Spectral clustering algorithms for planar shapes

Clustering algorithms are essential tools for exploring data structures and have applications in various fields of knowledge. Among them, spectral clustering, based on graph theory, stands out for its performance on non-convex data and has been the focus of extensive research. With technological advancements and the growing availability of geometric data, statistical shape analysis emerges as a promising approach to handle this type of information. This work proposes extensions of spectral algorithms for the analysis of 2D shapes as defined by Kendall. Versions incorporating Gaussian kernels, hierarchical methods, k-nearest neighbors, and similarity and dissimilarity measures between groups showed encouraging performance. The algorithms were tested in various simulation scenarios within the pre-shape space and on real data available in the literature. Algorithm performance was evaluated using the adjusted Rand index, demonstrating potential of the proposed methods.