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The DISCRIM Procedure

Example 25.5: Quadratic Discriminant Analysis of Remote-Sensing Data on Crops

In this example, PROC DISCRIM uses normal-theory methods (METHOD=NORMAL) assuming unequal variances (POOL=NO) for the remote-sensing data of Example 25.4. The PRIORS statement, PRIORS PROP, sets the prior probabilities proportional to the sample sizes. The CROSSVALIDATE option displays cross validation error-rate estimates. Note that the total error count estimate by cross validation (0.5556) is much larger than the total error count estimate by resubstitution (0.1111). The following statements produce Output 25.5.1:

   proc discrim data=crops
                method=normal pool=no
                crossvalidate;
      class Crop;
      priors prop;
      id xvalues;
      var x1-x4;
      title2 'Using Quadratic Discriminant Function';
   run;

Output 25.5.1: Quadratic Discriminant Function on Crop Data

Discriminant Analysis of Remote Sensing Data on Five Crops
Using Quadratic Discriminant Function

The DISCRIM Procedure

Observations 36 DF Total 35
Variables 4 DF Within Classes 31
Classes 5 DF Between Classes 4

Class Level Information
Crop Variable
Name
Frequency Weight Proportion Prior
Probability
Clover Clover 11 11.0000 0.305556 0.305556
Corn Corn 7 7.0000 0.194444 0.194444
Cotton Cotton 6 6.0000 0.166667 0.166667
Soybeans Soybeans 6 6.0000 0.166667 0.166667
Sugarbeets Sugarbeets 6 6.0000 0.166667 0.166667


Discriminant Analysis of Remote Sensing Data on Five Crops
Using Quadratic Discriminant Function

The DISCRIM Procedure

Within Covariance Matrix Information
Crop Covariance
Matrix Rank
Natural Log of
the
Determinant of
the
Covariance Matrix
Clover 4 23.64618
Corn 4 11.13472
Cotton 4 13.23569
Soybeans 4 12.45263
Sugarbeets 4 17.76293


Discriminant Analysis of Remote Sensing Data on Five Crops
Using Quadratic Discriminant Function

The DISCRIM Procedure

Generalized Squared Distance to Crop
From Crop Clover Corn Cotton Soybeans Sugarbeets
Clover 26.01743 1320 104.18297 194.10546 31.40816
Corn 27.73809 14.40994 150.50763 38.36252 25.55421
Cotton 26.38544 588.86232 16.81921 52.03266 37.15560
Soybeans 27.07134 46.42131 41.01631 16.03615 23.15920
Sugarbeets 26.80188 332.11563 43.98280 107.95676 21.34645


Discriminant Analysis of Remote Sensing Data on Five Crops
Using Quadratic Discriminant Function

The DISCRIM Procedure
Classification Summary for Calibration Data: WORK.CROPS
Resubstitution Summary using Quadratic Discriminant Function

Number of Observations and Percent Classified into Crop
From Crop Clover Corn Cotton Soybeans Sugarbeets Total
Clover 9
81.82
0
0.00
0
0.00
0
0.00
2
18.18
11
100.00
Corn 0
0.00
7
100.00
0
0.00
0
0.00
0
0.00
7
100.00
Cotton 0
0.00
0
0.00
6
100.00
0
0.00
0
0.00
6
100.00
Soybeans 0
0.00
0
0.00
0
0.00
6
100.00
0
0.00
6
100.00
Sugarbeets 0
0.00
0
0.00
1
16.67
1
16.67
4
66.67
6
100.00
Total 9
25.00
7
19.44
7
19.44
7
19.44
6
16.67
36
100.00
Priors 0.30556
 
0.19444
 
0.16667
 
0.16667
 
0.16667
 
 
 

Error Count Estimates for Crop
  Clover Corn Cotton Soybeans Sugarbeets Total
Rate 0.1818 0.0000 0.0000 0.0000 0.3333 0.1111
Priors 0.3056 0.1944 0.1667 0.1667 0.1667  


Discriminant Analysis of Remote Sensing Data on Five Crops
Using Quadratic Discriminant Function

The DISCRIM Procedure
Classification Summary for Calibration Data: WORK.CROPS
Cross-validation Summary using Quadratic Discriminant Function

Number of Observations and Percent Classified into Crop
From Crop Clover Corn Cotton Soybeans Sugarbeets Total
Clover 9
81.82
0
0.00
0
0.00
0
0.00
2
18.18
11
100.00
Corn 3
42.86
2
28.57
0
0.00
0
0.00
2
28.57
7
100.00
Cotton 3
50.00
0
0.00
2
33.33
0
0.00
1
16.67
6
100.00
Soybeans 3
50.00
0
0.00
0
0.00
2
33.33
1
16.67
6
100.00
Sugarbeets 3
50.00
0
0.00
1
16.67
1
16.67
1
16.67
6
100.00
Total 21
58.33
2
5.56
3
8.33
3
8.33
7
19.44
36
100.00
Priors 0.30556
 
0.19444
 
0.16667
 
0.16667
 
0.16667
 
 
 

Error Count Estimates for Crop
  Clover Corn Cotton Soybeans Sugarbeets Total
Rate 0.1818 0.7143 0.6667 0.6667 0.8333 0.5556
Priors 0.3056 0.1944 0.1667 0.1667 0.1667  

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