[Java] 数据分析--分类

ID3算法

思路：分类算法的输入为训练集，输出为对数据进行分类的函数。ID3算法为分类函数生成分类树
需求：对水果训练集的一个维度（是否甜）进行预测
实现：决策树，熵函数，ID3，weka库 J48类

ComputeGain.java

 1 public class ComputeGain {

 2     public static void main(String[] args) {

 3         System.out.printf("h(11,16) = %.4f%n", h(11,16));

 4         System.out.println("Gain(Size):");

 5         System.out.printf("\th(3,5) = %.4f%n", h(3,5));

 6         System.out.printf("\th(6,7) = %.4f%n", h(6,7));

 7         System.out.printf("\th(2,4) = %.4f%n", h(2,4));

 8         System.out.printf("\tg({3,6,2},{5,7,4}) = %.4f%n",

 9                     g(new int[]{3,6,2},new int[]{5,7,4}));

10         System.out.println("Gain(Color):");

11         System.out.printf("\th(3,4) = %.4f%n", h(3,4));

12         System.out.printf("\th(3,5) = %.4f%n", h(3,5));

13         System.out.printf("\th(2,3) = %.4f%n", h(2,3));

14         System.out.printf("\th(2,4) = %.4f%n", h(2,4));

15         System.out.printf("\tg({3,3,2,2},{4,5,3,4}) = %.4f%n",

16                     g(new int[]{3,3,2,2},new int[]{4,5,3,4}));

17         System.out.println("Gain(Surface):");

18         System.out.printf("\th(4,7) = %.4f%n", h(4,7));

19         System.out.printf("\th(4,6) = %.4f%n", h(4,6));

20         System.out.printf("\th(3,3) = %.4f%n", h(3,3));

21         System.out.printf("\tg({4,4,3},{7,6,3}) = %.4f%n",

22                     g(new int[]{4,4,3},new int[]{7,6,3}));

23         System.out.println("Gain(Size|SMOOTH):");

24         System.out.printf("\th(1,3) = %.4f%n", h(1,3));

25         System.out.printf("\th(3,3) = %.4f%n", h(3,3));

26         System.out.printf("\tg({1,3,0},{3,3,1}) = %.4f%n",

27                     g(new int[]{1,3,0},new int[]{3,3,1}));

28         System.out.println("Gain(Color|SMOOTH):");

29         System.out.printf("\th(2,3) = %.4f%n", h(2,3));

30         System.out.printf("\tg({2,2,0},{3,2,2}) = %.4f%n",

31                     g(new int[]{2,2,0},new int[]{3,2,2}));

32         System.out.println("Gain(Size|ROUGH):");

33         System.out.printf("\th(3,6) = %.4f%n", h(3,6));

34         System.out.printf("\th(1,2) = %.4f%n", h(1,2));

35         System.out.printf("\tg({2,1,1},{2,2,2}) = %.4f%n",

36                     g(new int[]{2,1,1},new int[]{2,2,2}));

37         System.out.println("Gain(Color|ROUGH):");

38         System.out.printf("\th(4,6) = %.4f%n", h(4,6));

39         System.out.printf("\tg({1,1,1},{2,2,2}) = %.4f%n",

40                     g(new int[]{1,0,2,1},new int[]{1,2,2,1}));

41     }

42

43     /*  Gain for the splitting {A1, A2, ...}, where Ai

44         has n[i] points, m[i] of which are favorable.

45     */

46     public static double g(int[] m, int[] n) {

47         int sm = 0, sn = 0;

48         double nsh = 0.0;

49         for (int i = 0; i < m.length; i++) {

50             sm += m[i];

51             sn += n[i];

52             nsh += n[i]*h(m[i],n[i]);

53         }

54         return h(sm, sn) - nsh/sn;

55     }

56

57     /*  Entropy for m favorable items out of n.

58     */

59     public static double h(int m, int n) {

60         if (m == 0 || m == n) {

61             return 0;

62         }

63         double p = (double)m/n, q = 1 - p;

64         return -p*lg(p) - q*lg(q);

65     }

66

67     /*  Returns the binary logarithm of x.

68     */

69     public static double lg(double x) {

70         return Math.log(x)/Math.log(2);

71     }

72 }

h(11,16) = 0.8960
Gain(Size):
h(3,5) = 0.9710
h(6,7) = 0.5917
h(2,4) = 1.0000
g({3,6,2},{5,7,4}) = 0.0838
Gain(Color):
h(3,4) = 0.8113
h(3,5) = 0.9710
h(2,3) = 0.9183
h(2,4) = 1.0000
g({3,3,2,2},{4,5,3,4}) = 0.0260
Gain(Surface):
h(4,7) = 0.9852
h(4,6) = 0.9183
h(3,3) = 0.0000
g({4,4,3},{7,6,3}) = 0.1206
Gain(Size|SMOOTH):
h(1,3) = 0.9183
h(3,3) = 0.0000
g({1,3,0},{3,3,1}) = 0.5917
Gain(Color|SMOOTH):
h(2,3) = 0.9183
g({2,2,0},{3,2,2}) = 0.5917
Gain(Size|ROUGH):
h(3,6) = 1.0000
h(1,2) = 1.0000
g({2,1,1},{2,2,2}) = 0.2516
Gain(Color|ROUGH):
h(4,6) = 0.9183
g({1,1,1},{2,2,2}) = 0.9183

 1 import weka.classifiers.trees.J48;

 2 import weka.core.Instances;

 3 import weka.core.Instance;

 4 import weka.core.converters.ConverterUtils.DataSource;

 5

 6 public class TestWekaJ48 {

 7     public static void main(String[] args) throws Exception {

 8         DataSource source = new DataSource("data/AnonFruit.arff");

 9         Instances instances = source.getDataSet();

10         instances.setClassIndex(3);  // target attribute: (Sweet)

11

12         J48 j48 = new J48();  // an extension of ID3

13         j48.setOptions(new String[]{"-U"});  // use unpruned tree

14         j48.buildClassifier(instances);

15

16         for (Instance instance : instances) {

17             double prediction = j48.classifyInstance(instance);

18             System.out.printf("%4.0f%4.0f%n",

19                     instance.classValue(), prediction);

20         }

21     }

22 }

1 1
1 1
1 1
1 0
1 1
0 0
1 1
0 0
0 0
0 0
1 1
1 1
1 1
1 1
0 0
1 1

贝叶斯分类

思路：基于训练集计算的比率生成的函数进行分类

Fruit.java

 1 import java.io.File;

 2 import java.io.FileNotFoundException;

 3 import java.util.HashSet;

 4 import java.util.Scanner;

 5 import java.util.Set;

 6

 7 public class Fruit {

 8     String name, size, color, surface;

 9     boolean sweet;

10

11     public Fruit(String name, String size, String color, String surface,

12             boolean sweet) {

13         this.name = name;

14         this.size = size;

15         this.color = color;

16         this.surface = surface;

17         this.sweet = sweet;

18     }

19

20     @Override

21     public String toString() {

22         return String.format("%-12s%-8s%-8s%-8s%s",

23                 name, size, color, surface, (sweet? "T": "F") );

24     }

25

26     public static Set<Fruit> loadData(File file) {

27         Set<Fruit> fruits = new HashSet();

28         try {

29             Scanner input = new Scanner(file);

30             for (int i = 0; i < 7; i++) {  // read past metadata

31                 input.nextLine();

32             }

33             while (input.hasNextLine()) {

34                 String line = input.nextLine();

35                 Scanner lineScanner = new Scanner(line);

36                 String name = lineScanner.next();

37                 String size = lineScanner.next();

38                 String color = lineScanner.next();

39                 String surface = lineScanner.next();

40                 boolean sweet = (lineScanner.next().equals("T"));

41                 Fruit fruit = new Fruit(name, size, color, surface, sweet);

42                 fruits.add(fruit);

43             }

44         } catch (FileNotFoundException e) {

45             System.err.println(e);

46         }

47         return fruits;

48     }

49

50     public static void print(Set<Fruit> fruits) {

51         int k=1;

52         for (Fruit fruit : fruits) {

53             System.out.printf("%2d. %s%n", k++, fruit);

54         }

55     }

56 }

BayesianTest.java

 1 import java.io.File;

 2 import java.util.Set;

 3

 4 public class BayesianTest {

 5     private static Set<Fruit> fruits;

 6

 7     public static void main(String[] args) {

 8         fruits = Fruit.loadData(new File("data/Fruit.arff"));

 9         Fruit fruit = new Fruit("cola", "SMALL", "RED", "SMOOTH", false);

10         double n = fruits.size();  // total number of fruits in training set

11         double sum1 = 0;           // number of sweet fruits

12         for (Fruit f : fruits) {

13             sum1 += (f.sweet? 1: 0);

14         }

15         double sum2 = n - sum1;    // number of sour fruits

16         double[][] p = new double[4][3];

17         for (Fruit f : fruits) {

18             if (f.sweet) {

19                 p[1][1] += (f.size.equals(fruit.size)? 1: 0)/sum1;

20                 p[2][1] += (f.color.equals(fruit.color)? 1: 0)/sum1;

21                 p[3][1] += (f.surface.equals(fruit.surface)? 1: 0)/sum1;

22             } else {

23                 p[1][2] += (f.size.equals(fruit.size)? 1: 0)/sum2;

24                 p[2][2] += (f.color.equals(fruit.color)? 1: 0)/sum2;

25                 p[3][2] += (f.surface.equals(fruit.surface)? 1: 0)/sum2;

26             }

27         }

28         double pc1 = p[1][1]*p[2][1]*p[3][1]*sum1/n;

29         double pc2 = p[1][2]*p[2][2]*p[3][2]*sum2/n;

30         System.out.printf("pc1 = %.4f, pc2 = %.4f%n", pc1, pc2);

31         System.out.printf("Predict %s is %s.%n",

32                 fruit.name, (pc1 > pc2? "sweet": "sour"));

33     }

34 }

pc1 = 0.0186, pc2 = 0.0150
Predict cola is sweet.

TestWekaBayes.java

 1 import java.util.List;

 2 import weka.classifiers.Evaluation;

 3 import weka.classifiers.bayes.NaiveBayes;

 4 import weka.classifiers.evaluation.Prediction;

 5 import weka.core.Instance;

 6 import weka.core.Instances;

 7 import weka.core.converters.ConverterUtils;

 8 import weka.core.converters.ConverterUtils.DataSource;

 9

10 public class TestWekaBayes {

11     public static void main(String[] args) throws Exception {

12 //        ConverterUtils.DataSource source = new ConverterUtils.DataSource("data/AnonFruit.arff");

13         DataSource source = new DataSource("data/AnonFruit.arff");

14         Instances train = source.getDataSet();

15         train.setClassIndex(3);  // target attribute: (Sweet)

16         //build model

17         NaiveBayes model=new NaiveBayes();

18         model.buildClassifier(train);

19

20         //use

21         Instances test = train;

22         Evaluation eval = new Evaluation(test);

23         eval.evaluateModel(model,test);

24         List <Prediction> predictions = eval.predictions();

25         int k = 0;

26         for (Instance instance : test) {

27             double actual = instance.classValue();

28             double prediction = eval.evaluateModelOnce(model, instance);

29             System.out.printf("%2d.%4.0f%4.0f", ++k, actual, prediction);

30             System.out.println(prediction != actual? " *": "");

31         }

32     }

33 }

1. 1 1
2. 1 1
3. 1 1
4. 1 1
5. 1 1
6. 0 1 *
7. 1 1
8. 0 0
9. 0 0
10. 0 1 *
11. 1 1
12. 1 1
13. 1 1
14. 1 1
15. 0 0
16. 1 1

SVM算法

思路：生成超平面方程，计算数据点位于哪一边

逻辑回归

思路：将目标值属性为布尔值的问题转化成一个数值变量，在转化后的问题上进行线性回归
需求：某政党候选人想知道选举获胜的花费
实现

 1 import org.apache.commons.math3.analysis.function.*;

 2 import org.apache.commons.math3.stat.regression.SimpleRegression;

 3

 4 public class LogisticRegression {

 5     static int n = 6;

 6     static double[] x = {5, 15, 25, 35, 45, 55};

 7     static double[] p = {2./6,2./5, 4./8, 5./9, 3./5, 4./5};

 8     static double[] y = new double[n];    // y = logit(p)

 9

10     public static void main(String[] args) {

11

12         //  Transform p-values into y-values:

13         Logit logit = new Logit();

14         for (int i = 0; i < n; i++) {

15             y[i] = logit.value(p[i]);

16         }

17

18         //  Set up input array for linear regression:

19         double[][] data = new double[n][n];

20         for (int i = 0; i < n; i++) {

21             data[i][0] = x[i];

22             data[i][1] = y[i];

23         }

24

25         //  Run linear regression of y on x:

26         SimpleRegression sr = new SimpleRegression();

27         sr.addData(data);

28

29         //  Print results:

30         for (int i = 0; i < n; i++) {

31             System.out.printf("x = %2.0f, y = %7.4f%n", x[i], sr.predict(x[i]));

32         }

33         System.out.println();

34

35         //  Convert y-values back to p-values:

36         Sigmoid sigmoid = new Sigmoid();

37         for (int i = 0; i < n; i++) {

38             double p = sr.predict(x[i]);

39             System.out.printf("x = %2.0f, p = %6.4f%n", x[i], sigmoid.value(p));

40         }

41     }

42 }

x = 5, y = -0.7797
x = 15, y = -0.4067
x = 25, y = -0.0338
x = 35, y = 0.3392
x = 45, y = 0.7121
x = 55, y = 1.0851

x = 5, p = 0.3144
x = 15, p = 0.3997
x = 25, p = 0.4916
x = 35, p = 0.5840
x = 45, p = 0.6709
x = 55, p = 0.7475

k临近

思路：根据临近范围内的样本进行分类

 1 import weka.classifiers.lazy.IBk;  // K-Nearest Neighbors

 2 import weka.core.Instances;

 3 import weka.core.Instance;

 4 import weka.core.converters.ConverterUtils.DataSource;

 5

 6 public class TestIBk {

 7     public static void main(String[] args) throws Exception {

 8         DataSource source = new DataSource("data/AnonFruit.arff");

 9         Instances instances = source.getDataSet();

10         instances.setClassIndex(3);  // target attribute: (Sweet)

11

12         IBk ibk = new IBk();

13         ibk.buildClassifier(instances);

14

15         for (Instance instance : instances) {

16             double prediction = ibk.classifyInstance(instance);

17             System.out.printf("%4.0f%4.0f%n",

18                     instance.classValue(), prediction);

19         }

20     }

21 }

1 1
1 1
1 1
1 0
1 1
0 0
1 1
0 0
0 0
0 0
1 1
1 1
1 1
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0 0
1 1

巴特西

[Java] 数据分析--分类

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