The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

Linear discriminant analysis (LDA) has been an active topic of research during the last century. However, the existing algorithms have several limitations when applied to visual data. LDA is only optimal for Gaussian distributed classes with equal covariance matrices, and only classes-1 features can be extracted. On the other hand, LDA does not scale well to high dimensional data (over-fitting), and it cannot handle optimally multimodal distributions. In this paper, we introduce Multimodal Oriented Discriminant Analysis (MODA), an LDA extension which can overcome these drawbacks. A new formulation and several novelties are proposed:

1) An optimal dimensionality reduction for multimodal Gaussian classes with different covariances is derived. The new criteria allows for extracting more than classes-1 features. 2) A covariance approximation is introduced to improve generalization and avoid over-fitting when dealing with high dimensional data. 3) A linear time iterative majorization method is suggested in order to find a local optimum.

Several synthetic and real experiments on face recognition show that MODA outperform existing LDA techniques.

Keywords

Dimensionality reduction, Subspace methods, Discriminative modeling, Face Recognition

Notes

Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Associated Lab(s) / Group(s): People Image Analysis Consortium, MultiRobot Lab, Human Identification at a Distance, Face Group

Associated Project(s): Camera Assisted Meeting Event Observer and Component Analysis for Data Analysis

Number of pages: 22

Text Reference

Fernando De la Torre Frade and Takeo Kanade, "Multimodal Oriented Discriminant Analysis," tech. report CMU-RI-TR-05-03, Robotics Institute, Carnegie Mellon University, January, 2005

BibTeX Reference

@techreport{De_la_Torre_Frade_2005_4906,
   author = "Fernando {De la Torre Frade} and Takeo Kanade",
   title = "Multimodal Oriented Discriminant Analysis",
   booktitle = "",
   institution = "Robotics Institute",
   month = "January",
   year = "2005",
   number= "CMU-RI-TR-05-03",
   address= "Pittsburgh, PA",
}

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