Fisher’s Linear Discriminant  Find a direction and project all data points onto that direction such that:  The points in the same class are as close.

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Fisher’s Linear Discriminant  Find a direction and project all data points onto that direction such that:  The points in the same class are as close as possible  The centers of these two classes are as far as possible

Fisher’s Linear Discriminant

Variance between-class The centers of these two classes are as far as possible

Variances within-class The points in the same class are as close as possible

Rayleigh Coefficient  Rayleigh coefficient with respect to is defined as  Linear Fisher ’ s discriminant is generated by maximizing the Rayleigh coefficient  How about the nonlinear Fisher ’ s discriminant?