Dresden 2017 – scientific programme

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BP: Fachverband Biologische Physik

BP 24: Posters - Protein Structure and Dynamics

BP 24.17: Poster

Tuesday, March 21, 2017, 14:00–16:00, P1A

Principal Component Analysis of Circular Data: Theory and Application — •Florian Sittel, Thomas Filk, and Gerhard Stock — Uni Freiburg/Brsg.

Principal Component Analysis (PCA) is a widely adopted technique for dimensionality reduction. However, being a linear transform it is not directly applicable to circular data, like the dynamics of protein backbone dihedral angles. There have been several attempts already in modifying PCA to circular data (Dihedral angle-based PCA, GeoPCA, Principal Geodesic Analysis), yet none addressed the special geometry of the underlying space (N-dimensional Tori) to full extent, resulting in projection errors. Here we present a theoretical analysis of this geometry and identify the pitfalls given by the periodicity of the data. Based on our analysis, we derive a new formulation of PCA of circular data and demonstrate its performance in the context of protein dynamics.