Fisher s Linear Discriminant Function p g i X X M X p X i g m g i X m X i x X m x x x m m 0, i x x m x v x i y m y v SS between ( v x v x ) i
A g ( v x ) i i { v ( m m) }{ v ( m m) } v i vav ( m m)( m m) i ( m m)( m m) v ( m m)( m m) SS within g ( v x v x ) i g { v ( X ) m v ( m m) } g { v ( X m )} g { v ( X m )}{ v ( X m )} v, i vwv W g ( X m )( X m ) v ( X m )( X m ) i
Q 0 SS SS between within v Av v Wv Q0 v Wv ( v ) Q v Av λ Wv Q Q Av λwv v Av λwv v W W ULU ( ) / UL UL / Av λ UL / / ( UL ) A ( UL ) / / ( UL ) v / / { } ( UL ) v ( UL ) v / / ( UL ) A ( UL ) { } ( ) {( ) } / / UL A UL λ ( UL ) / v UL / A UL λ { } / ( ) ( ) λ v v Av λ v Wv SSbetween v Av Q 0 λ SS v within Wv λ 0 n n λ λ L λ n 3
v θ y ( ) v x v ( X m) θ g ( ) ( y ) i, i v, i { v ( X m) } v ( X m) { } ( X m)( X m) v v T v T g i ( X m)( X m) factor f y θ ( ) ( ) θ v x v θ b ( X m) ( X m) b θ v / 4
X x z D / diag x D / diag ( X m) D diag diag T z f ( ) ( ) s s ( ), i, i, i z z z z, i f ( ) ( b x ) / ( D z ) z diag D / diag b b Rc R z z, i c D / diag b S ( ) ( n) [ s L s ] R C [ c L ] RC c n [ c L ] c n 5
n χ p + χ g log Λ df ( p )( g ) Λ n + + p X g λ 0 PDiscrim.dpr.. Add Data Add Var. 6
Del Data Del Var...3.3 Save(CVS) 7
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. ID χ p factor.8 Discrimination Factors Structure Matrix 5
Cooley,W.W. and Lohnes,P.R. (97) Multivariate data analysis. Wiley. Mardia,K.V., Kent,J.T. and Bibby,J.M. (979) Multivariate analysis. Academic Press. Overall,J.E. and Klett,C.J. (97) Applied multivariate analysis. McGraw-Hill Boo Company. 6