Human Action Classification Using Multidimensional Functional Data Analysis Method

In this paper, we describe a novel approach that can classify a human action by using a multidimensional functional data analysis (MFDA) and the Cartesian product of reproducing kernel Hilbert spaces (CPRKHSs). The main idea is to represent the human action video dataset into a multidimensional functional data framework, and then apply the mathematical properties of CPRKPHS to classify these datasets. First, we extract the feature vector that can properly describe the shape of the human action from each frame of a given video. Here, a set of features extracted from a given video can be expressed as a multivariate functional data format depending on an order of time. Since a multidimensional functional data belongs to the non-linear manifold, we embed a multidimensional functional data into the CPRKPHS by using the idea of kernel methods. Then, we have shown that the geodesic distance between two human actions on manifold can be approximate with the product Hilbert norm for a difference between two multidimensional functional datasets in RKPHS. Finally, we have applied common classification rules such as the k-NN method based on these distances in order to classify a human action.