Principal component analysis and clustering on manifolds
The paper studies the problem of principal component analysis (PCA) and clustering on manifolds. The authors review related literature and depict advances in the important topics of PCA and clustering on manifolds. They deal here mostly with two key manifolds, namely spheres and tori. The paper is organized as follows. After introducing notation and terminology in Section 2, a comprehensive introduction to torus PCA is given in Section 3, which is followed by the description of a new method of clustering for manifold data, namely MINCE post AGE (Mode huntIng on the main principle Nested small Circle of prE-clusters post Adaptive linkaGe clustEring), in Section 4 where the authors cover three typical applications. The first two address SARS-CoV-2 structure clustering on the microscopic level of backbone suites using torus PCA and on a mesoscopic level using PNS (Principal Nested Shape analysis) on lifts to the pre-shape sphere of shape spaces. Using simulated data from a benchmark algorithm, the last application illustrates how to apply the method to Euclidean data. One of the simplest model based methods for torus PCA is to use the wrapped multivariate normal distribution following indirectly a multivariate normal formulation for Euclidean PCA. However, this method is not yet well explored. This is briefly presented in Section 5. The paper is concluded with an overview addressing some important research questions.
scientific article; zbMATH DE number 7451367
scientific article