Since HOOF features are histograms and do not lie in a Euclidean space, we cannot model HOOF time series as Linear Dynamical Systems. Instead, we model the temporal evolution of HOOF features using a linear-state non-linear dynamical system using kernels on the space of histograms,
where Φ is an implicit map of a kernel on the space of histograms. Some of the metrics that can be used with the kernel are the Bhattacharrya
distance, the Histogram Intersection kernel, and the Minimum Distance Pairwise Assignment. Using Kernel PCA, we identify the parameters ymean
, A, B and the covariance of the noise processes v and w, as well as the kernel principal components that represent the C function.