In a NDA, the between-class and the within-class Laplacian scatter matrix are designed from sample to sample, respectively, to characterize the between-class separability and the within-class compactness by seeking for discriminant matrix to simultaneously maximize the between-class Laplacian scatter and minimize the within-class Laplacian scatter.
The key idea is that we seek the optimal model parameters, including the transformation matrix, via the joint optimization of MI function and log-likelihood function, therefore, this method can not only reduce the estimation errors but also maximize the between-class separability.
In an MMDA, the within-class graph and between-class graph are, respectively, designed to characterize the within-class compactness and the between-class separability, seeking for the discriminant matrix to simultaneously maximize the between-class scatter and minimize the within-class scatter.
The projection w should minimize the within-class distance and maximize the between-class distance simultaneously.
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.
This method regards each voxel value as a possible threshold and tests whether a given threshold will maximize the between-class variance [20, 29].
The linear discriminant analysis (LDA) is able to maximize the between-class distance and minimize the within-class distance simultaneously [21].
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.
The core of OMMPS is to maximize the between-class margin by increasing the between-class scatter distance and reducing the within-class scatter distance simultaneously.
