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The variance between class1 and class 2 from gray level 0 to 255 is computed recursively, so a gray level value,, which maximized the between-class variance can be obtained.
We calculated these metrics for between three and eight groups, and both metrics indicated that separating the samples into five groups minimized the within-group sample distance and maximized the between-group distance.
This involved successive binary partitioning of the data set by identifying at each partition the explanatory variable which maximized the between-groups sum-of-squares using analysis of variance.
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.
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|.
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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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com