This animation uses scatter diagrams and small matrices to build within-class scatter S_W, between-class scatter S_B, and total scatter S_T = S_W + S_B from probability-weighted definitions. Using teaching matrices S_W = diag(2,1) and S_B = diag(2,3), it reveals four separability scores one at a time: the trace ratio (5/3), generalized trace tr(S_W^-1 S_B) (4), determinant ratio (8), and a two-class Gaussian Bhattacharyya distance (0.5). It stresses these numbers are not comparable across criteria, helping first-year AI students connect geometric intuition to explicit formulas used in feature evaluation.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
# Four separability scores measure different aspects of class structure Explain four explicitly chosen feature-evaluation criteria using scatter diagrams and small matrices. Define within-class scatter S_W, between-class scatter S_B, and total scatter S_T = S_W + S_B using consistent probability-weighted definitions. For the multiclass teaching matrices S_W = diag(2,1) and S_B = diag(2,3), calculate the trace ratio tr(S_B)/tr(S_W) = 5/3, the generalized trace tr(S_W inverse S_B) = 4, and the determinant ratio det(S_T)/det(S_W) = 8. Require positive-definite S_W for the inverse and determinant examples. In a separate two-class Gaussian example, compare N(0,1) with N(2,1), obtaining Bhattacharyya distance 0.5. Do not compare these four numerical magnitudes as if they shared a common performance scale. Explain that each criterion ranks candidate representations under its own assumptions. Use black backgrounds and reveal one score at a time. Useful for connecting geometric separability to explicit formulas. Audience: 一年级人工智能专业学生