独角兽企业重金招聘Python工程师标准>>>
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
*
* @param primary
*原始二维数组矩阵
* @return 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
*
* @param matrix
*中心化后的矩阵
* @return 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
*
* @param 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
