Clustering on Grassmann manifolds via kernel embedding with application to action analysis

With the aim of improving the clustering of data (such as image sequences) lying on Grassmann manifolds, we propose to embed the manifolds into Reproducing Kernel Hilbert Spaces. To this end, we define a measure of cluster distortion and embed the manifolds such that the distortion is minimised. We show that the optimal solution is a generalised eigenvalue problem that can be solved very efficiently. Experiments on several clustering tasks (including human action clustering) show that in comparison to the recent intrinsic Grassmann k-means algorithm, the proposed approach obtains notable improvements in clustering accuracy, while also being several orders of magnitude faster.