Fisher's (1936) Iris data is often used for benchmarking classification algorithms. It consists of the following continuous input attributes and a classification target:
This example trains a Naive Bayes classifier using 140 of the 150 continuous patterns, then classifies ten unknown plants using their sepal and petal measurements.
import com.imsl.datamining.*;
import com.imsl.stat.NormalDistribution;
import java.io.*;
public class NaiveBayesClassifierEx1 {
private static double[][] irisFisherData = {
{1.0, 5.1, 3.5, 1.4, .2}, {1.0, 4.9, 3.0, 1.4, .2},
{1.0, 4.7, 3.2, 1.3, .2}, {1.0, 4.6, 3.1, 1.5, .2},
{1.0, 5.0, 3.6, 1.4, .2}, {1.0, 5.4, 3.9, 1.7, .4},
{1.0, 4.6, 3.4, 1.4, .3}, {1.0, 5.0, 3.4, 1.5, .2},
{1.0, 4.4, 2.9, 1.4, .2}, {1.0, 4.9, 3.1, 1.5, .1},
{1.0, 5.4, 3.7, 1.5, .2}, {1.0, 4.8, 3.4, 1.6, .2},
{1.0, 4.8, 3.0, 1.4, .1}, {1.0, 4.3, 3.0, 1.1, .1},
{1.0, 5.8, 4.0, 1.2, .2}, {1.0, 5.7, 4.4, 1.5, .4},
{1.0, 5.4, 3.9, 1.3, .4}, {1.0, 5.1, 3.5, 1.4, .3},
{1.0, 5.7, 3.8, 1.7, .3}, {1.0, 5.1, 3.8, 1.5, .3},
{1.0, 5.4, 3.4, 1.7, .2}, {1.0, 5.1, 3.7, 1.5, .4},
{1.0, 4.6, 3.6, 1.0, .2}, {1.0, 5.1, 3.3, 1.7, .5},
{1.0, 4.8, 3.4, 1.9, .2}, {1.0, 5.0, 3.0, 1.6, .2},
{1.0, 5.0, 3.4, 1.6, .4}, {1.0, 5.2, 3.5, 1.5, .2},
{1.0, 5.2, 3.4, 1.4, .2}, {1.0, 4.7, 3.2, 1.6, .2},
{1.0, 4.8, 3.1, 1.6, .2}, {1.0, 5.4, 3.4, 1.5, .4},
{1.0, 5.2, 4.1, 1.5, .1}, {1.0, 5.5, 4.2, 1.4, .2},
{1.0, 4.9, 3.1, 1.5, .2}, {1.0, 5.0, 3.2, 1.2, .2},
{1.0, 5.5, 3.5, 1.3, .2}, {1.0, 4.9, 3.6, 1.4, .1},
{1.0, 4.4, 3.0, 1.3, .2}, {1.0, 5.1, 3.4, 1.5, .2},
{1.0, 5.0, 3.5, 1.3, .3}, {1.0, 4.5, 2.3, 1.3, .3},
{1.0, 4.4, 3.2, 1.3, .2}, {1.0, 5.0, 3.5, 1.6, .6},
{1.0, 5.1, 3.8, 1.9, .4}, {1.0, 4.8, 3.0, 1.4, .3},
{1.0, 5.1, 3.8, 1.6, .2}, {1.0, 4.6, 3.2, 1.4, .2},
{1.0, 5.3, 3.7, 1.5, .2}, {1.0, 5.0, 3.3, 1.4, .2},
{2.0, 7.0, 3.2, 4.7, 1.4}, {2.0, 6.4, 3.2, 4.5, 1.5},
{2.0, 6.9, 3.1, 4.9, 1.5}, {2.0, 5.5, 2.3, 4.0, 1.3},
{2.0, 6.5, 2.8, 4.6, 1.5}, {2.0, 5.7, 2.8, 4.5, 1.3},
{2.0, 6.3, 3.3, 4.7, 1.6}, {2.0, 4.9, 2.4, 3.3, 1.0},
{2.0, 6.6, 2.9, 4.6, 1.3}, {2.0, 5.2, 2.7, 3.9, 1.4},
{2.0, 5.0, 2.0, 3.5, 1.0}, {2.0, 5.9, 3.0, 4.2, 1.5},
{2.0, 6.0, 2.2, 4.0, 1.0}, {2.0, 6.1, 2.9, 4.7, 1.4},
{2.0, 5.6, 2.9, 3.6, 1.3}, {2.0, 6.7, 3.1, 4.4, 1.4},
{2.0, 5.6, 3.0, 4.5, 1.5}, {2.0, 5.8, 2.7, 4.1, 1.0},
{2.0, 6.2, 2.2, 4.5, 1.5}, {2.0, 5.6, 2.5, 3.9, 1.1},
{2.0, 5.9, 3.2, 4.8, 1.8}, {2.0, 6.1, 2.8, 4.0, 1.3},
{2.0, 6.3, 2.5, 4.9, 1.5}, {2.0, 6.1, 2.8, 4.7, 1.2},
{2.0, 6.4, 2.9, 4.3, 1.3}, {2.0, 6.6, 3.0, 4.4, 1.4},
{2.0, 6.8, 2.8, 4.8, 1.4}, {2.0, 6.7, 3.0, 5.0, 1.7},
{2.0, 6.0, 2.9, 4.5, 1.5}, {2.0, 5.7, 2.6, 3.5, 1.0},
{2.0, 5.5, 2.4, 3.8, 1.1}, {2.0, 5.5, 2.4, 3.7, 1.0},
{2.0, 5.8, 2.7, 3.9, 1.2}, {2.0, 6.0, 2.7, 5.1, 1.6},
{2.0, 5.4, 3.0, 4.5, 1.5}, {2.0, 6.0, 3.4, 4.5, 1.6},
{2.0, 6.7, 3.1, 4.7, 1.5}, {2.0, 6.3, 2.3, 4.4, 1.3},
{2.0, 5.6, 3.0, 4.1, 1.3}, {2.0, 5.5, 2.5, 4.0, 1.3},
{2.0, 5.5, 2.6, 4.4, 1.2}, {2.0, 6.1, 3.0, 4.6, 1.4},
{2.0, 5.8, 2.6, 4.0, 1.2}, {2.0, 5.0, 2.3, 3.3, 1.0},
{2.0, 5.6, 2.7, 4.2, 1.3}, {2.0, 5.7, 3.0, 4.2, 1.2},
{2.0, 5.7, 2.9, 4.2, 1.3}, {2.0, 6.2, 2.9, 4.3, 1.3},
{2.0, 5.1, 2.5, 3.0, 1.1}, {2.0, 5.7, 2.8, 4.1, 1.3},
{3.0, 6.3, 3.3, 6.0, 2.5}, {3.0, 5.8, 2.7, 5.1, 1.9},
{3.0, 7.1, 3.0, 5.9, 2.1}, {3.0, 6.3, 2.9, 5.6, 1.8},
{3.0, 6.5, 3.0, 5.8, 2.2}, {3.0, 7.6, 3.0, 6.6, 2.1},
{3.0, 4.9, 2.5, 4.5, 1.7}, {3.0, 7.3, 2.9, 6.3, 1.8},
{3.0, 6.7, 2.5, 5.8, 1.8}, {3.0, 7.2, 3.6, 6.1, 2.5},
{3.0, 6.5, 3.2, 5.1, 2.0}, {3.0, 6.4, 2.7, 5.3, 1.9},
{3.0, 6.8, 3.0, 5.5, 2.1}, {3.0, 5.7, 2.5, 5.0, 2.0},
{3.0, 5.8, 2.8, 5.1, 2.4}, {3.0, 6.4, 3.2, 5.3, 2.3},
{3.0, 6.5, 3.0, 5.5, 1.8}, {3.0, 7.7, 3.8, 6.7, 2.2},
{3.0, 7.7, 2.6, 6.9, 2.3}, {3.0, 6.0, 2.2, 5.0, 1.5},
{3.0, 6.9, 3.2, 5.7, 2.3}, {3.0, 5.6, 2.8, 4.9, 2.0},
{3.0, 7.7, 2.8, 6.7, 2.0}, {3.0, 6.3, 2.7, 4.9, 1.8},
{3.0, 6.7, 3.3, 5.7, 2.1}, {3.0, 7.2, 3.2, 6.0, 1.8},
{3.0, 6.2, 2.8, 4.8, 1.8}, {3.0, 6.1, 3.0, 4.9, 1.8},
{3.0, 6.4, 2.8, 5.6, 2.1}, {3.0, 7.2, 3.0, 5.8, 1.6},
{3.0, 7.4, 2.8, 6.1, 1.9}, {3.0, 7.9, 3.8, 6.4, 2.0},
{3.0, 6.4, 2.8, 5.6, 2.2}, {3.0, 6.3, 2.8, 5.1, 1.5},
{3.0, 6.1, 2.6, 5.6, 1.4}, {3.0, 7.7, 3.0, 6.1, 2.3},
{3.0, 6.3, 3.4, 5.6, 2.4}, {3.0, 6.4, 3.1, 5.5, 1.8},
{3.0, 6.0, 3.0, 4.8, 1.8}, {3.0, 6.9, 3.1, 5.4, 2.1},
{3.0, 6.7, 3.1, 5.6, 2.4}, {3.0, 6.9, 3.1, 5.1, 2.3},
{3.0, 5.8, 2.7, 5.1, 1.9}, {3.0, 6.8, 3.2, 5.9, 2.3},
{3.0, 6.7, 3.3, 5.7, 2.5}, {3.0, 6.7, 3.0, 5.2, 2.3},
{3.0, 6.3, 2.5, 5.0, 1.9}, {3.0, 6.5, 3.0, 5.2, 2.0},
{3.0, 6.2, 3.4, 5.4, 2.3}, {3.0, 5.9, 3.0, 5.1, 1.8}
};
public static void main(String[] args) throws Exception {
/* Data corrections described in the KDD data mining archive */
irisFisherData[34][4] = 0.1;
irisFisherData[37][2] = 3.1;
irisFisherData[37][3] = 1.5;
/* Train first 140 patterns of the iris Fisher Data */
int[] irisClassificationData = new int[irisFisherData.length-10];
double[][] irisContinuousData =
new double[irisFisherData.length-10][irisFisherData[0].length - 1];
for (int i = 0; i < irisFisherData.length-10; i++) {
irisClassificationData[i] = (int) irisFisherData[i][0] - 1;
System.arraycopy(irisFisherData[i], 1,
irisContinuousData[i], 0, irisFisherData[0].length - 1);
}
int nNominal =0; /* no nominal input attributes */
int nContinuous =4; /* four continuous input attributes */
int nClasses =3; /* three classification categories */
NaiveBayesClassifier nbTrainer =
new NaiveBayesClassifier(nContinuous, nNominal, nClasses);
for (int i=0; i<nContinuous; i++)
nbTrainer.createContinuousAttribute(new NormalDistribution());
nbTrainer.train(irisContinuousData, irisClassificationData );
int[][] classErrors = nbTrainer.getTrainingErrors();
System.out.println(" Iris Classification Training Error Rates");
System.out.println("------------------------------------------------");
System.out.println(" Setosa Versicolour Virginica | Total");
System.out.println(" "+classErrors[0][0]+"/"+classErrors[0][1]+
" "+classErrors[1][0]+"/"+classErrors[1][1]+" "+
classErrors[2][0]+"/"+classErrors[2][1]+" | "+
classErrors[3][0]+"/"+classErrors[3][1]);
System.out.println(
"------------------------------------------------\n\n\n");
/* Classify last 10 iris data patterns with the trained classifier */
double[] continuousInput = new double[(irisFisherData[0].length - 1)];
double[] classifiedProbabilities = new double[nClasses];
System.out.println("Probabilities for Incorrect Classifications");
System.out.println(" Predicted ");
System.out.println(
" Class | Class | P(0) P(1) P(2) ");
System.out.println(
"-------------------------------------------------------");
for (int i=0; i<10; i++) {
int targetClassification =
(int)irisFisherData[(irisFisherData.length-10)+i][0] - 1;
System.arraycopy(irisFisherData[(irisFisherData.length-10) +i], 1,
continuousInput, 0, (irisFisherData[0].length - 1));
classifiedProbabilities =
nbTrainer.probabilities(continuousInput, null);
int classification = nbTrainer.predictClass(continuousInput, null);
if ( classification == 0 ) System.out.print("Setosa |");
else if (classification == 1) System.out.print("Versicolour |");
else if (classification == 2) System.out.print("Virginica |");
else System.out.print("Missing |");
if (targetClassification == 0) System.out.print(" Setosa |");
else if (targetClassification == 1)
System.out.print(" Versicolour |");
else if (targetClassification == 2)
System.out.print(" Virginica |");
else System.out.print(" Missing |");
for (int j=0; j<nClasses; j++) {
Object[] pArgs = {new Double(classifiedProbabilities[j])};
System.out.printf(" %2.3f ", pArgs);
}
System.out.println();
}
}
}
The Naive Bayes classifier incorrectly classifies 6 of the 150 training patterns.
Iris Classification Training Error Rates
------------------------------------------------
Setosa Versicolour Virginica | Total
0/50 0/50 20/40 | 20/140
------------------------------------------------
Probabilities for Incorrect Classifications
Predicted
Class | Class | P(0) P(1) P(2)
-------------------------------------------------------
Virginica | Virginica | 0.000 0.436 0.564
Virginica | Virginica | 0.000 0.466 0.534
Versicolour | Virginica | 0.000 0.542 0.458
Virginica | Virginica | 0.000 0.441 0.559
Virginica | Virginica | 0.000 0.412 0.588
Virginica | Virginica | 0.000 0.466 0.534
Versicolour | Virginica | 0.000 0.542 0.458
Versicolour | Virginica | 0.000 0.515 0.485
Virginica | Virginica | 0.000 0.460 0.540
Versicolour | Virginica | 0.000 0.551 0.449
Link to Java source.