An animation walks through Fisher's linear discriminant analysis using two small point clouds (class A and class B) on a black background. It computes class means, builds the within-class scatter matrix S_W, and derives the optimal projection direction w. Both clouds are projected onto this line, showing separated means and a threshold boundary. Two test points are classified by their projected values. Useful for first-year AI students learning how linear discriminant analysis reduces classification to a 1D projection problem.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
# Computing Fisher's best direction from eight points Place class A at (0,0), (2,0), (0,2), and (2,2), and class B at (4,2), (6,2), (4,4), and (6,4). Calculate their means as (1,1) and (5,3), and show that each unnormalized within-class scatter matrix is 4I, so S_W = 8I. Transform the Fisher optimization into the direction w proportional to S_W inverse times the mean difference. Choose w = (0.5,0.25) and project both clouds onto it. Their projected means become 0.75 and 3.25. For this example, choose their midpoint 2 as the threshold, producing the boundary 2x1 + x2 = 8. Test (3,1), which projects to 1.75, and (3,3), which projects to 2.25. Explain that the midpoint threshold is an explicit example choice, not a universal consequence of Fisher's criterion. Use black backgrounds and consistent cyan and orange classes. Audience: 一年级人工智能专业学生