判別分析 - cfme.chiba-u.jp

1 1 2 3 px() N( ) 1 xm196 vxm ()/ m 196 xm xxmm 196. duxmM / m 196. xm xdxmM222 ()/ dM Mahalanobis 4 px() )(112mx 2Md)]())((21exp[)()2(])(21exp[21)(122/12 2/12mxmxmxxp )(1xp)(2xp2Md xm)]())((2p[)()(1x2xM)]()(21exp[)2()(121 1mxCmxCx Tp 2x2m22Md2Md 11 dm2)]()(21exp[)2()(122mxCmxCx Tp m1x12Md5 )}()(2{1})(){(122222122221mxmxDD G1G2)2)((2)}()(2{1212122221212mmxmmmmmm D1D22 0x xxm1m2xxm2()xm2()mm x0 Dxm1212 () Dxm2222 ()

2 Mm12 if x xmmthen x G 01222, if x xmmthen x G 012122, 22212 DDifGx 22211212 DDifGx6 G12,04,1212221 mm G21m2mx 7 ,G1,G2 x2p2()x G2 G1G2m21m22G21p1()x G x1m11m12 x11112 mvariable group, 8 x1 G1 x2 G2 x2 G2 G1G2m21m22 G1 G21x1 x1 G2 x2 G1 m11m12x1 11129 x2 x DD DE1DE2 DDEE12 G1 xpp21()()

3 Xx G2 x G2 x110 x2 1112121222 mmmmxmmm111122 mmm221222 fxxxm(, ) ()()12111122 11 x1xm()()211222220 )]()(21exp[)2()(1112111mxCmxCx Tp 2)]()(21exp[)2()(2122112mxCmxCx Tp 11 y )]()(21exp[)2()(1112111mxCmxCx Tp 11ab'xy)]()(21exp[)2()(2122112mxCmxCx Tp 11 a'b'ab ab ''x)]()(1exp[)2()]()(21exp[)2()()(121111 121121mxCmxCmxCmxCxx TTpp 11211)(1)()(GpGpp xxxx )}]()()(){(21exp[)]()(2exp[)2()(21211122 22mxCmxmxCmxmxCmxC TTp 2211)()(Gpp xxx2)(){(21)()(log1111Tp mxCmxx2210)(1)(lGDDp x )(1)}()( )(){(2)(g22212112 TDDp mxCmxx222,21,1122,21,210)(21)()(log0)(2) ()(logGDDpGDDppMMMM xxxx )(22,1,MMDD ,,22)(px 12 DT12111()()()xxmCxm T21fD D()()()xxx 2212 DT22212() ()()xxmCxm fTT()()()()()xxmCxmxmCxm 11f(x) C,m1,m2 fTTT TTTTT()()()()(){}xxmCxmxmCxmxCxxCmmCxmCm xCxxCmmCxmCm 221111221212111 1 TTTT{}()()()xCxxCmmCxmCmxCmmmmCxCC 111 111212111 x TTTT()()mCmmCmxCmm 11121211212 1T C aTCb=bTCa T{()mmCm 1211 ()}()mmCmxCmm12121122TT ()()()()}

4 MmCmmxmCmm121121122TT mmm 12213 )()(2)(211mmCmxx Tf 111212221122121211 CCC )()(2)(211 fTmmCmxx)()(2,21,22,11,11112122212121 mmmmmmxxTC)(1211112122212121 mmxxTC)])(())([(21111222212122111 mxmxC14 2 (I) x2(I) m2AB x1m1 22100 C 1mm =[x1,x2]T v2 AB v 220 2m vxmvxm1111 ()/()/ v1 v1v2vxm2222 ()/ Dxmx m222112222 ()() (Euclid) Dvv2122211122222 ()() D (Euclid) Dxm xmE2112222 ()( ) DDEAEB,,22 15 2 (II) (II) x2k1k2 2 2 m2 1 12 12211 Cmmm1 x1 1 22122 , Cmm k1k2 2 22100 kCu 12222212122212 kkuuD 20 vk111 / D u2vk222 / u116 x x2m2x1 x2 x1m121x'xm Hotelling x2k1k2xxm u 1m2k1kUx' 1u2uT][21uuU whitening)

5 X1m1x2v2 m2v1vCk k12/ x1m1DT22 vvv17 D2 D2 ' D2 DTT21212 vv// D2 x'xm kUx' CUCUkT kTkkTk12121212 CkCkCUxmCUxm()(()) ()////kUx TTkTkTTk12121 xmUCCU xmxmUCUxm()() ()()()// 222100 kC TTTT11 xmUUCUU xmxmCxm()()()()() 12/12/1/100/1 kkCkCv ()() UUT 1 2/10 kk 1111/0/1 kk CUCUUCUkTT 11111()()UUT 1 2222//10 kk DT22 vvvUCUUCUT 1()18