Multifactor Analysis Based on Factor-Dependent Geometry

This paper proposes a novel method that preserves the geometrical structure created by variation of multiple factors in analysis of multiple factor models, i.e., multifactor analysis. We use factor-dependent submanifolds as constituent elements of the factor-dependent geometry in a multiple factor framework. In this paper, a submanifold is defined as some subset of a manifold in the data space, and factor-dependent submanifolds are defined as the submanifolds created for each factor by varying only this factor. In this paper, we show that MPCA is formulated using factordependent submanifolds, as is our proposed method. We show, however, that MPCA loses the original shapes of these submanifolds because MPCA’s parameterization is based on averaging the shapes of factor-dependent submanifolds for each factor. On the other hand, our proposed multifactor analysis preserves the shapes of individual factordependent submanifolds in low-dimensional spaces. Because the parameters obtained b...

• Type: Journal
• Year: 2011
• Where: CVPR
• Authors: Sung Won Park
• Keywords: Computer Vision, CVPR 2011, Factor-dependent Submanifolds, Factordependent Submanifolds, Multiple Factor