A Backward Generalization of PCA for Exploration and Feature Extraction of Manifold-Valued Shapes

A generalized Principal Component Analysis (PCA) for manifold-valued shapes is discussed with forward and backward stepwise views of PCA. Finite and infinite dimensional shape spaces are briefly introduced. A backward extension of PCA for the shape spaces, called Principal Nested Spheres, is shown in more detail, which results in a non-geodesic decomposition of shape spaces, capturing more variation in lower dimension.