Fréchet mean-based Grassmann discriminant analysis

Abstract

Representing image sets and videos with Grassmann manifold has become popular due to its powerful capability to extract discriminative information in machine learning research. However, existing techniques operations on Grassmann manifold are usually suffering from the problem of computational expensive, thus the application range of Grassmann manifold is limited. In this paper, we propose the Frechet mean-based Grassmann discriminant analysis (FMGDA) algorithm to implement the videos (or image sets) data dimensionality reduction and clustering task. The data dimensionality reduction algorithm proposed by us can not only be used to reduce Grassmann data from high-dimensional data to a relative low-dimensional data, but also to maximize between-class distance and minimize within-class distance simultaneously. Frechet mean is used to characterize the clustering center of Grassmann manifold space. We further show that the learning problem can be expressed as a trace ratio problem which can be efficiently solved. We designed a detailed experimental scheme to test the performance of our proposed algorithm, and the tests were assessed on several benchmark data sets. The experimental results indicate that our approach leads to a significant improvement over state-of-the-art methods.