Article ID Journal Published Year Pages File Type
536231 Pattern Recognition Letters 2015 7 Pages PDF
Abstract

•Necessary and sufficient conditions for separability of 1DLDA are derived.•The commonly used separable scatter model is proved as a special case.•Separability of the MVLDA operator is proved.•1DLDA and 2DLDA solutions are theoretically related and compared.•Zigzag sorting procedure is proposed for row & column-sorted 2DLDA features.

Two-directional (2D) variants of the linear discriminant analysis (LDA) algorithm have been widely used to extract features of matrix-variate signals. This paper derives the theoretical relationship between 2DLDA and one-directional (1D) LDA based on the separable transformation framework. Separable transforms such as separable 2DDCT are widely used for image compression in the JPEG standard; therefore, a similar framework for 2DLDA provides the corresponding parallel foundation for separable image feature extraction. There are existing 2DLDA methods providing a separable transformation, however they are not directly related to the 1DLDA solution. We will derive a 2DLDA method as a matrix-variate representation of a separable 1DLDA operator. Furthermore, we derive the necessary and sufficient conditions for separability of 1DLDA. These conditions will be helpful to clarify both limitations and advantages of 2DLDA. Also, a 2DLDA framework in parallel to 2DDCT allows us to exploit related techniques developed for 2DDCT, such as the feature selection procedure.

Related Topics
Physical Sciences and Engineering Computer Science Computer Vision and Pattern Recognition
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