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DA maximizes the between group - within group variance.
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LDA computes a transformation that maximizes the between-class scatter while minimizing the within-class scatter by maximizing the following ratio: det|SB|/det|SW|.
Thus, the design of an efficient face recognition algorithm requires judicious construction of a feature vector that maximizes the between-person variability, while minimizing the within-person variability across 2D spatial coordinates of an image as well as changing conditions of image capturing.
This maximizes the between-region differences with respect to geographic, cultural, and social-economic characteristics, and therefore allows us to capture a sample that is homogeneous within regions and heterogeneous among regions.
The projection w should minimize the within-class distance and maximize the between-class distance simultaneously.
This turns out to be the same as maximizing the between-class variance.
The goal of LDA is to maximize the between-class measure while minimizing the within-class measure.
Specifically, Equation 12 tries to minimize the within-class distance and maximize the between-class distance simultaneously.
Furthermore, instead of directly maximizing the between-class distance, a new constraint w′ mk+1−m k )≥ρ (k=1,2,⋯,K−1) is introduced.
The aim of OMMPS is to maximize the between-class margin by increasing the between-class scatter distance and reducing the within-class scatter distance simultaneously.
The proposed method is able to maximize the between-class margin by increasing the between-class scatter distance and reducing the within-class scatter distance simultaneously.
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