Shape Component Analysis: Structure-preserving Dimension Reduction on Biological Shape Spaces

Abstract

Quantitative shape analysis is required by a wide range of biological studies over diverse scales, ranging from molecules to cells and organisms. In particular, high-throughput and systems-level studies of biological structures and functions have started to produce large volume of complex high-dimensional shape data. Analysis and understanding of high-dimensional biological shape data require dimension reduction techniques. We developed a technique for nonlinear dimension reduction of 2D and 3D biological shape representations on their Riemannian spaces. A key feature of this technique is that it preserves distances between different shapes in the embedded low-dimensional shape space. We demonstrate an application of this technique by combining it with nonlinear mean-shift clustering on the Riemannian spaces for unsupervised clustering of shapes of cellular organelles and proteins.