A dimensionality reduction method for high-dimensional circular data is developed, which is
based on a principal component analysis (PCA) of data points on a torus. Adopting a
geometrical view of PCA, various distance measures on a torus are introduced and the
associated problem of projecting data onto the principal subspaces is discussed. The main
idea is that the (periodicity-induced) projection error can be minimized by transforming the
data such that the maximal gap of the sampling is shifted to the periodic boundary. In a …