Semi-supervised Hessian Eigenmap for Human Action Recognition

Abstract

Dimensionality reduction has been attracting emerging attention with the explosive growing of high-dimensional data in many areas including web image annotation, video object detection, and human action recognition. Comparing with the traditional nonlinear dimensional reduction such as Locally Linear Embedding, Isometric feature Mapping, Laplacian Eigenmap, semi-supervised nonlinear dimensional reduction method can improve stability of the solution by taking into account prior information. In this paper, we integrate exact mapping information of certain data points into Hessian Eigenmap and propose semi-supervised Hessian Eigenmap. Considering the prior information with physical meaning, semi-supervised Hessian Eigenmap can approximate global low dimensional coordinates. On the other hand, Hessian can exploit high-order information of the local geometry of data distribution in comparison with graph Laplacian and thus further boost the performance. We conduct experiments on both synthetic and real world datasets. The experimental results demonstrate that the proposed semi-supervised Hessian Eigenmap algorithm outperforms the representative semi-supervised Laplacian Eigenmap algorithm.