# Fisher Discriminant Analysis

Fisher Discriminant Analysis

The 30 round points are data. The 15 red points were generated from a normal distribution with mean , the 15 blue ones with mean , and in both cases the covariance matrix was the identity matrix. The problem is to classify or predict the color using the inputs and .

{1.2,0}

{0,1.2}

x

1

x

2

Fisher linear discriminant analysis determines a canonical direction for which the data is most separated when projected on a line in this direction. The solid gray line shows the canonical direction.

The squares are projected points on a line inclined at the angle with respect to the origin. When is adjusted so the projected points are aligned with the gray line, the points are maximally separated in the sense that the ratio of between-classes variances to within-classes variance is maximized.

θ

θ

A point is predicted as red or blue according to whether its projection on the canonical direction lies closest to the projected mean of the red or blue data points.