导入jar包:Jama-1.0.2.jar
//========计算类===========
import java.util.ArrayList;
import java.util.Collections; import java.util.HashMap; import java.util.Iterator; import java.util.List; import java.util.Map; import java.util.Map.Entry; import java.util.TreeMap;import Jama.Matrix;
/*
* 算法步骤: * 1)将原始数据按列组成n行m列矩阵X * 2)特征中心化。即每一维的数据都减去该维的均值，使每一维的均值都为0 * 3)求出协方差矩阵 * 4)求出协方差矩阵的特征值及对应的特征向量 * 5)将特征向量按对应的特征值大小从上往下按行排列成矩阵，取前k行组成矩阵p * 6)Y=PX 即为降维到k维后的数据 */ public class PCA {private static final double threshold = 0.95;// 特征值阈值
/**
* * 使每个样本的均值为0 * * primary * 原始二维数组矩阵 * averageArray 中心化后的矩阵 */ public double[][] changeAverageToZero(double[][] primary) { int n = primary.length; int m = primary[0].length; double[] sum = new double[m]; double[] average = new double[m]; double[][] averageArray = new double[n][m]; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { sum[i] += primary[j][i]; } average[i] = sum[i] / n; } for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { averageArray[j][i] = primary[j][i] - average[i]; } } return averageArray; }/**
* * 计算协方差矩阵 * * matrix * 中心化后的矩阵 * result 协方差矩阵 */ public double[][] getVarianceMatrix(double[][] matrix) { int n = matrix.length;// 行数 int m = matrix[0].length;// 列数 double[][] result = new double[m][m];// 协方差矩阵 for (int i = 0; i < m; i++) { for (int j = 0; j < m; j++) { double temp = 0; for (int k = 0; k < n; k++) { temp += matrix[k][i] * matrix[k][j]; } result[i][j] = temp / (n - 1); } } return result; }/**
* 求特征值矩阵 * * matrix * 协方差矩阵 * @return result 向量的特征值二维数组矩阵 */ public double[][] getEigenvalueMatrix(double[][] matrix) { Matrix A = new Matrix(matrix); // 由特征值组成的对角矩阵,eig()获取特征值 A.eig().getD().print(10, 6); double[][] result = A.eig().getD().getArray(); return result; }/**
* 标准化矩阵（特征向量矩阵） * * @param matrix * 特征值矩阵 * @return result 标准化后的二维数组矩阵 */ public double[][] getEigenVectorMatrix(double[][] matrix) { Matrix A = new Matrix(matrix); A.eig().getV().print(6, 2); double[][] result = A.eig().getV().getArray(); return result; }/**
* 寻找主成分 * * @param prinmaryArray * 原始二维数组数组 * @param eigenvalue * 特征值二维数组 * @param eigenVectors * 特征向量二维数组 * @return principalMatrix 主成分矩阵 */ public Matrix getPrincipalComponent(double[][] primaryArray, double[][] eigenvalue, double[][] eigenVectors) { Matrix A = new Matrix(eigenVectors);// 定义一个特征向量矩阵 double[][] tEigenVectors = A.transpose().getArray();// 特征向量转置 Map<Integer, double[]> principalMap = new HashMap<Integer, double[]>();// key=主成分特征值，value=该特征值对应的特征向量 TreeMap<Double, double[]> eigenMap = new TreeMap<Double, double[]>( Collections.reverseOrder());// key=特征值，value=对应的特征向量；初始化为翻转排序，使map按key值降序排列 double total = 0;// 存储特征值总和 int index = 0, n = eigenvalue.length; double[] eigenvalueArray = new double[n];// 把特征值矩阵对角线上的元素放到数组eigenvalueArray里 for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (i == j) eigenvalueArray[index] = eigenvalue[i][j]; } index++; }for (int i = 0; i < tEigenVectors.length; i++) {
double[] value = new double[tEigenVectors[0].length]; value = tEigenVectors[i]; eigenMap.put(eigenvalueArray[i], value); }// 求特征总和
for (int i = 0; i < n; i++) { total += eigenvalueArray[i]; } // 选出前几个主成分 double temp = 0; int principalComponentNum = 0;// 主成分数 List<Double> plist = new ArrayList<Double>();// 主成分特征值 for (double key : eigenMap.keySet()) { if (temp / total <= threshold) { temp += key; plist.add(key); principalComponentNum++; } } System.out.println("\n" + "当前阈值: " + threshold); System.out.println("取得的主成分数: " + principalComponentNum + "\n");// 往主成分map里输入数据
for (int i = 0; i < plist.size(); i++) { if (eigenMap.containsKey(plist.get(i))) { principalMap.put(i, eigenMap.get(plist.get(i))); } }// 把map里的值存到二维数组里
double[][] principalArray = new double[principalMap.size()][]; Iterator<Entry<Integer, double[]>> it = principalMap.entrySet() .iterator(); for (int i = 0; it.hasNext(); i++) { principalArray[i] = it.next().getValue(); }Matrix principalMatrix = new Matrix(principalArray);
return principalMatrix;
}/**
* 矩阵相乘 * * @param primary * 原始二维数组 * * @param matrix * 主成分矩阵 * * @return result 结果矩阵 */ public Matrix getResult(double[][] primary, Matrix matrix) { Matrix primaryMatrix = new Matrix(primary); Matrix result = primaryMatrix.times(matrix.transpose()); return result; } }//==================MainClass========================
import Jama.Matrix;
public class PCAMain {
public static void main(String[] args) { PCA pca = new PCA(); double[][] primaryArray = { { 100, 2, 3, 4, 1, 2, 32, 2 }, { 1, 2, 31, 52, 1, 2, 32, 2 }, { 1, 2, 32, 2, 1, 2, 31, 52 }, { 1, 2, 32, 2, 1, 2, 30, 52 } }; System.out.println("--------------------------------------------"); System.out.println("原始数据: "); System.out.println(primaryArray.length + "行，" + primaryArray[0].length + "列"); for (int i = 0; i < primaryArray.length; i++) { for (int j = 0; j < primaryArray[0].length; j++) { System.out.print(+primaryArray[i][j] + " \t"); } System.out.println(); }// 均值中心化后的矩阵
double[][] averageArray = pca.changeAverageToZero(primaryArray); System.out.println("--------------------------------------------"); System.out.println("均值0化后的数据: "); System.out.println(averageArray.length + "行，" + averageArray[0].length + "列"); for (int i = 0; i < averageArray.length; i++) { for (int j = 0; j < averageArray[0].length; j++) { System.out.print((float) averageArray[i][j] + " \t"); } System.out.println(); } // 协方差矩阵 double[][] varMatrix = pca.getVarianceMatrix(averageArray); System.out.println("---------------------------------------------"); System.out.println("协方差矩阵: "); for (int i = 0; i < varMatrix.length; i++) { for (int j = 0; j < varMatrix[0].length; j++) { System.out.print((float) varMatrix[i][j] + "\t"); } System.out.println(); } // 特征值矩阵 System.out.println("--------------------------------------------"); System.out.println("特征值矩阵: "); double[][] eigenvalueMatrix = pca.getEigenvalueMatrix(varMatrix);// 特征向量矩阵
System.out.println("--------------------------------------------"); System.out.println("特征向量矩阵: "); double[][] eigenVectorMatrix = pca.getEigenVectorMatrix(varMatrix);// 主成分矩阵
System.out.println("--------------------------------------------"); Matrix principalMatrix = pca.getPrincipalComponent(primaryArray, eigenvalueMatrix, eigenVectorMatrix); System.out.println("主成分矩阵: "); principalMatrix.print(6, 2);// 降维后的矩阵
System.out.println("--------------------------------------------"); System.out.println("降维后的矩阵: "); Matrix resultMatrix = pca.getResult(primaryArray, principalMatrix); resultMatrix.print(10, 2);}
}
直接可运行