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1 () 11-1 ()Classification Analysis( ) m() p.d.f prior (decision) (loss function) Bayes Risk for any decision d( ) posterior risk posterior risk Posterior prob. j (uniform prior) where Mahalanobis Distance(M-distance)

2 () 11-2 ( ) (score) Quadratic Discriminant Score Liner Discriminant score= score (1) (2) posterior prob. M-distance quadratic discriminant score posterior prob. M-distance linear discriminant score (m = 2 )

3 () 11-3 (1)/* */ DATA IRIS; TITLE ''; INPUT SEPALLEN SEPALWID PETALLEN PETALWID SPEC_NO IF SPEC_NO=1 then SPECIES='SETOSA'; IF SPEC_NO=2 then SPECIES='VERSICOLOR'; IF SPEC_NO=3 then SPECIES='VIRGINICA'; DROP SPEC_NO; /*LABEL SEPALLEN=SEPAL LENGTH IN MM. SEPALWID=SEPAL WIDTH IN MM. PETALLEN=PETAL LENGTH IN MM. PETALWID=PETAL WIDTH IN MM.;*/ cards; proc discrim simple wcov wcorr pcov pcorr listerr pool=test; class species; run; 150 Observations 149 DF Total 4 Variables 147 DF Within Classes 3 Classes 2 DF Between Classes Class Level Information Prior SPECIES Frequency Weight Proportion Probability SETOSA VERSIC VIRGIN

4 () 11-4 Within Class Covariance Matrices SPECIES = SETOSA DF = 49 SEPALLEN SEPALWID PETALLEN PETALWID SPECIES = VERSIC DF = 49 SEPALLEN SEPALWID PETALLEN PETALWID SPECIES = VIRGIN DF = 49 SEPALLEN SEPALWID PETALLEN PETALWID Pooled Within Class Covariance Matrix DF = 147 SEPALLEN SEPALWID PETALLEN PETALWID Within Class Correlation Coefficients / Prob > R SPECIES = SETOSA SEPALLEN SEPALWID PETALLEN

5 () PETALWID SPECIES = VERSIC SEPALLEN SEPALWID PETALLEN PETALWID SPECIES = VIRGIN SEPALLEN SEPALWID PETALLEN PETALWID Pooled Within Class Correlation Coefficients / Prob > R SEPALLEN SEPALWID PETALLEN PETALWID Simple Statistics Total Sample Variable N Sum Mean Variance Std Dev SEPALLEN SEPALWID PETALLEN

6 () 11-6 PETALWID SPECIES = SETOSA Variable N Sum Mean Variance Std Dev SEPALLEN SEPALWID PETALLEN PETALWID SPECIES = VERSIC Variable N Sum Mean Variance Std Dev SEPALLEN SEPALWID PETALLEN PETALWID SPECIES = VIRGIN Variable N Sum Mean Variance Std Dev SEPALLEN SEPALWID PETALLEN PETALWID Within Covariance Matrix Information Covariance Natural Log of the Determinant SPECIES Matrix Rank of the Covariance Matrix SETOSA VERSIC VIRGIN Pooled Test of Homogeneity of Within Covariance Matrices Notation: K = Number of Groups

7 () 11-7 P N = Number of Variables = Total Number of Observations Number of Groups N(i) = Number of Observations in the i'th Group 1 Within SS Matrix(i) V = Pooled SS Matrix N(i)/2 N/ P + 3P 1 RHO = 1.0 SUM _ N(i) N _ 6(P+1)(K 1) DF =.5(K 1)P(P+1) PN/2 N V Under null hypothesis: 2 RHO ln PN(i)/2 _ N(i) _ is distributed approximately as chi square(df) Test Chi Square Value = with 20 DF Prob > Chi Sq = Since the chi square value is significant at the the within covariance matrices will be used in the discriminant function. 0.1 level, Reference: Morrison, D.F. (1976) Multivariate Statistical Methods p252. Pairwise Generalized Squared Distances Between Groups 2 1 D (i j) = (X X )' COV (X X ) + ln COV i j j i j j Generalized Squared Distance to SPECIES From SPECIES SETOSA VERSIC VIRGIN SETOSA VERSIC VIRGIN

8 () 11-8 Classification Results for Calibration Data: WORK.IRIS Resubstitution Results using Quadratic Discriminant Function Generalized Squared Distance Function: 2 _ 1 _ D (X) = (X X )' COV (X X ) + ln COV j j j j j Posterior Probability of Membership in each SPECIES: 2 2 Pr(j X) = exp(.5 D (X)) / SUM exp(.5 D (X)) j k k Posterior Probability of Membership in SPECIES: Obs From Classified SPECIES into SPECIES SETOSA VERSIC VIRGIN 5 VIRGIN VERSIC * VERSIC VIRGIN * VERSIC VIRGIN * * Misclassified observation Classification Summary for Calibration Data: WORK.IRIS Resubstitution Summary using Quadratic Discriminant Function Generalized Squared Distance Function: 2 _ 1 _ D (X) = (X X )' COV (X X ) + ln COV j j j j j Posterior Probability of Membership in each SPECIES: 2 2 Pr(j X) = exp(.5 D (X)) / SUM exp(.5 D (X)) j k k Number of Observations and Percent Classified into SPECIES: From SPECIES SETOSA VERSIC VIRGIN Total SETOSA VERSIC VIRGIN

9 () Total Percent Priors Error Count Estimates for SPECIES: SETOSA VERSIC VIRGIN Total Rate Priors (2) /**/ DATA CROPS; TITLE 'REMOTE SENSING DATA ON FIVE CROPS'; INPUT CROP $ 1-10 X1-X4 XVALUES $ 12-22; CARDS; CORN CORN CORN CORN CORN CORN CORN SOYBEANS SOYBEANS SOYBEANS SOYBEANS SOYBEANS SOYBEANS COTTON COTTON COTTON COTTON COTTON COTTON SUGARBEETS SUGARBEETS SUGARBEETS SUGARBEETS SUGARBEETS SUGARBEETS CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER CLOVER ; PROC DISCRIM DATA=CROPS POOL=YES LIST OUT=CROPCAL; CLASS CROP; ID XVALUES; VAR X1-X4; TITLE2 'CLASSIFICATION OF CROP DATA'; DATA TEST; INPUT CROP $ 1-10 X1-X4 XVALUES $ 12-22; CARDS;

10 () ; PROC DISCRIM DATA=CROPCAL TESTDATA=TEST TESTLIST; CLASS CROP; TESTCLASS CROP; TESTID XVALUES; VAR X1-X4; TITLE2 'CLASSIFICATION OF TEST DATA'; RUN;

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國家圖書館典藏電子全文

國家圖書館典藏電子全文 M08916017 2002.12 1 1.1 1 1.2 2 1.3 2 1.4 3 1.5 4 6 2.1 6 2.2 8 2.2.1 8 2.2.2 15 2.3 20 2.4 24 2.4.1 26 2.4.2 30 2.5 31 2.5.1 31 2.5.2 35 38 3.1 38 3.1.1 38 3.1.2 39 3.1.3 40 I 3.1.4 41 3.1.5 44 3.1.6