iPGA: incremental principal geodesic analysis with applications to movement disorder classification.

The nonlinear version of the well known PCA called the Prinicipal Geodesic Analysis (PGA) was introduced in the past decade for statistical analysis of shapes as well as diffusion tensors. PGA of diffusion tensor fields or any other manifold-valued fields can be a computationally demanding task due to the dimensionality of the problem and thus establishing motivation for an incremental PGA (iPGA) algorithm. In this paper, we present a novel iPGA algorithm that incrementally updates the current Karcher mean and the principal sub-manifolds with any newly introduced data into the pool without having to recompute the PGA from scratch. We demonstrate substantial computational and memory savings of iPGA over the batch mode PGA for diffusion tensor fields via synthetic and real data examples. Further, we use the iPGA derived representation in an NN classifier to automatically discriminate between controls, Parkinson's Disease and Essential Tremor patients, given their HARDI brain scans.