CSE555: Introduction to Pattern Recognition Midterm ... - CEDAR

Appendix: Useful formulas.• For a 2 × 2 matrix,A =[a bc dthe matrix inverse isA −1 = 1 [ ]d −b=|A| −c a]1ad − bc[d −b−c a]• The scatter matrices S i are defined asS i = ∑x∈D i(x − m i )(x − m i ) twhere m i is the d-dimensional sample mean.The within-class scatter matrix is defined asS W = S 1 + S 2The between-class scatter matrix is defined asS B = (m 1 − m 2 )(m 1 − m 2 ) tThe solution for the w that optimizes J(w) = wt S B ww t S W w isw = S −1W (m 1 − m 2 )8