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A novel linear discriminant criterion function is proved to be equal to Fisher's criterion function. The analysis of the function is linked to spectral decomposition of the Laplacian of a graph. Moreover, the function is maximized using two algorithms. Experimental results show the effectiveness and some specific characteristics of our algorithms.
In this paper, an algorithm for nonlinear discriminant mapping (NDM) is presented, which elegantly integrates the ideas of both linear discriminant analysis (LDA) and Isomap by using the Laplacian of a graph. The objective of NDM is to find a linear subspace project of nonlinear data set, which preserves maximum difference between between-class scatter and within-class scatter.
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