• 算法步驟:
• 1)將原始數據按列組成n行m列矩陣X
• 2)特征中心化。即每一維的數據都減去該維的均值，使每一維的均值都為0
• 3)求出協方差矩陣
• 4)求出協方差矩陣的特征值及對應的特征向量
• 5)將特征向量按對應的特征值大小從上往下按行排列成矩陣，取前k行組成矩陣p
• 6)Y=PX 即為降維到k維后的數據

PCA

/** 算法步驟:* 1)將原始數據按列組成n行m列矩陣X* 2)特征中心化。即每一維的數據都減去該維的均值，使每一維的均值都為0* 3)求出協方差矩陣* 4)求出協方差矩陣的特征值及對應的特征向量* 5)將特征向量按對應的特征值大小從上往下按行排列成矩陣，取前k行組成矩陣p* 6)Y=PX 即為降維到k維后的數據*/
public class PCA {public static DenseMatrix64F runPCA(DenseMatrix64F src,int k) {DenseMatrix64F rs = new DenseMatrix64F(src.numRows,k);//計算輸入矩陣每個元素和特征值平均的差值矩陣DenseMatrix64F norm_X = new DenseMatrix64F(src.numRows,src.numCols);for(int i =0;i<src.numCols;i++) {double tmp=0;for(int j=0;j<src.numRows;j++) {tmp+=src.get(j, i);}tmp /=src.numRows;for(int j=0;j<src.numRows;j++) {norm_X.set(j,i, src.get(j, i)-tmp);}}//計算協方差矩陣DenseMatrix64F norm_X_T = new DenseMatrix64F(src.numCols,src.numRows);CommonOps.transpose(norm_X, norm_X_T);DenseMatrix64F scatter_matrix = new DenseMatrix64F(src.numCols,src.numCols);CommonOps.mult(norm_X_T,norm_X,scatter_matrix);//特征向量分解EDInfo ed = JacobiCount(new DenseMatrix64F(scatter_matrix),0.001,1000);//選取前k個特征DenseMatrix64F feature = new DenseMatrix64F(k,src.numCols);for(int i=0;i<k;i++) {for(int j=0;j<src.numCols;j++) {feature.set(i, j, ed.getValues().get(j, i));}}DenseMatrix64F feature_T = new DenseMatrix64F(src.numCols,k);CommonOps.transpose(feature, feature_T);CommonOps.mult(norm_X,feature_T,rs);return rs;}public static EDInfo JacobiCount(DenseMatrix64F src, double diff, int iter) {DenseMatrix64F values = new DenseMatrix64F(src.numRows,src.numCols);for(int i=0;i<src.numRows;i++) {for(int j=0;j<src.numCols;j++) {if(i == j) {values.set(i, j, 1);}else {values.set(i, j, 0);}}}int nCount = 0;while(true){double dbMax = Double.MIN_VALUE;int nRow = 0;int nCol = 1;for(int i=0;i<src.numRows;i++) {for(int j=0;j<src.numCols;j++) {if(i != j && Math.abs(src.get(i, j)) > dbMax) {dbMax = Math.abs(src.get(i, j));nRow = i;nCol = j;}}}if(dbMax < diff)break;if(nCount > iter)break;nCount++;double dbApp = src.get(nRow, nRow);double dbApq = src.get(nRow, nCol);double dbAqq = src.get(nCol, nCol);double dbAngle = 0.5*Math.atan2(-2*dbApq,dbAqq-dbApp);double dbSinTheta = Math.sin(dbAngle);double dbCosTheta = Math.cos(dbAngle);double dbSin2Theta = Math.sin(2*dbAngle);double dbCos2Theta = Math.cos(2*dbAngle);src.set(nRow, nRow, dbApp*dbCosTheta*dbCosTheta +dbAqq*dbSinTheta*dbSinTheta + 2*dbApq*dbCosTheta*dbSinTheta);src.set(nCol, nCol, dbApp*dbSinTheta*dbSinTheta +dbAqq*dbCosTheta*dbCosTheta - 2*dbApq*dbCosTheta*dbSinTheta);src.set(nRow, nCol, 0.5*(dbAqq-dbApp)*dbSin2Theta + dbApq*dbCos2Theta);src.set(nCol, nRow,src.get(nRow, nCol));for(int i = 0; i < src.numRows; i ++){if((i!=nCol) && (i!=nRow)){dbMax = src.get(i, nRow);src.set(i, nRow,src.get(i, nCol)*dbSinTheta+dbMax*dbCosTheta);src.set(i, nCol,src.get(i, nCol)*dbCosTheta-dbMax*dbSinTheta);}}for (int j = 0; j < src.numRows; j ++){if((j!=nCol) && (j!=nRow)){dbMax = src.get(nRow, j);src.set(nRow, j,src.get(nCol, j)*dbSinTheta+dbMax*dbCosTheta);src.set(nCol, j,src.get(nCol, j)*dbCosTheta-dbMax*dbSinTheta);}}for(int i = 0; i < src.numRows; i ++){dbMax = values.get(i,nRow);values.set(i, nRow,values.get(i,nCol)*dbSinTheta+dbMax*dbCosTheta);values.set(i,nCol,values.get(i,nCol)*dbCosTheta-dbMax*dbSinTheta);}}double[] eig = new double[src.numRows];for(int i=0;i<src.numRows;i++) {eig[i] = src.get(i, i);}int[] sortInx = argsort(eig);DenseMatrix64F tmpValues = new DenseMatrix64F(src.numRows,src.numCols);for(int i=0;i<src.numRows;i++) {for(int j=0;j<src.numRows;j++) {tmpValues.set(i, j, values.get(j,sortInx[i]));}eig[i] = src.get(sortInx[i],sortInx[i]);}for(int i = 0; i < src.numRows; i ++){double dSumVec = 0;for(int j = 0; j < src.numRows; j ++)dSumVec += tmpValues.get(j, i);if(dSumVec<0){for(int j = 0;j < src.numRows; j ++)tmpValues.set(j, i,tmpValues.get(j, i)*-1);}}return new EDInfo(tmpValues,eig);}public static int[] argsort(double[] input) {int[] rs =  new int[input.length];for(int i=0;i<input.length;i++){rs[i] = i;}for(int i=0;i<input.length-1;i++) {for(int j=i+1;j<input.length;j++) {if(input[i] < input[j]) {double tmp = input[i];int tmpIndex = rs[j];input[i] = input[j];input[j] = tmp;rs[j] = rs[i];rs[i] = tmpIndex;}}}return rs;}static ArrayList<String> tempc=new ArrayList<>();public  double[][] readData() throws IOException {double[][] res=new double[78][13];try { // 防止文件建立或讀取失敗，用catch捕捉錯誤并打印，也可以throw/* 讀入TXT文件 */File filename = new File("src/bp/test.txt"); // 要讀取以上路徑的input。txt文件InputStreamReader reader = new InputStreamReader(new FileInputStream(filename)); // 建立一個輸入流對象readerBufferedReader br = new BufferedReader(reader); // 建立一個對象，它把文件內容轉成計算機能讀懂的語言String line = "";line = br.readLine();int j=0;while (line != null) {String[] temp=line.split(",");for(int i=0;i<13;i++){res[j][i]=Double.parseDouble(temp[i]);System.out.print( res[j][i]+" ");}tempc.add(temp[13]);System.out.println();j++;line = br.readLine();}} catch (Exception e) {e.printStackTrace();}return res;}public static void writeTxt( DenseMatrix64F denseMatrix64F){try { // 防止文件建立或讀取失敗，用catch捕捉錯誤并打印，也可以throw/* 讀入TXT文件 */StringBuilder stringBuilder=new StringBuilder();for(int i=0;i<denseMatrix64F.numRows;i++){for(int j=0;j<denseMatrix64F.numCols;j++)stringBuilder.append(denseMatrix64F.get(i,j)).append(',');stringBuilder.append(tempc.get(i)).append("\n");}File writename = new File("src/bp/test(low).txt"); // 相對路徑，如果沒有則要建立一個新的output。txt文件writename.createNewFile(); // 創建新文件BufferedWriter out = new BufferedWriter(new FileWriter(writename));out.write(stringBuilder.toString()); // \r\n即為換行out.flush(); // 把緩存區內容壓入文件out.close(); // 最后記得關閉文件} catch (Exception e) {e.printStackTrace();}}public static void main(String[] args) throws IOException {// TODO Auto-generated catch blockPCA pca = new PCA();//獲得樣本集double[][] primaryArray =pca.readData() ;System.out.println();DenseMatrix64F denseMatrix64F=runPCA(new DenseMatrix64F(primaryArray),10);writeTxt(denseMatrix64F);}}

最小最大規范化

public class DealData {static double[] max=new double[14];static double[] min=new double[14];static ArrayList<String> list1=new ArrayList<>();public static  List<List<Double>> readTxt(String fileName){List<List<Double>> list=new ArrayList<>();Arrays.fill(max,Integer.MIN_VALUE);Arrays.fill(min,Integer.MAX_VALUE);try { // 防止文件建立或讀取失敗，用catch捕捉錯誤并打印，也可以throw/* 讀入TXT文件 */File filename = new File(fileName); // 要讀取以上路徑的input。txt文件InputStreamReader reader = new InputStreamReader(new FileInputStream(filename)); // 建立一個輸入流對象readerBufferedReader br = new BufferedReader(reader); // 建立一個對象，它把文件內容轉成計算機能讀懂的語言String line = "";line = br.readLine();while (line != null) {if(line.length()>0){String[] temp=line.split(",");ArrayList<Double> strings=new ArrayList<>();for(int i=0;i<temp.length-1;i++){strings.add(Double.parseDouble(temp[i]));max[i]=Math.max(Double.parseDouble(temp[i]),max[i]);min[i]=Math.min(Double.parseDouble(temp[i]),min[i]);}list1.add(temp[temp.length-1]);list.add(strings);}line = br.readLine();}} catch (Exception e) {e.printStackTrace();}return list;}public static void writeTxt(String content){try { // 防止文件建立或讀取失敗，用catch捕捉錯誤并打印，也可以throw/* 讀入TXT文件 */File writename = new File("src/bp/trainBayes.txt"); // 相對路徑，如果沒有則要建立一個新的output。txt文件writename.createNewFile(); // 創建新文件BufferedWriter out = new BufferedWriter(new FileWriter(writename));out.write(content); // \r\n即為換行out.flush(); // 把緩存區內容壓入文件out.close(); // 最后記得關閉文件} catch (Exception e) {e.printStackTrace();}}public static void main(String[] args) {List<List<Double>> list=   readTxt("src/bp/train(low).txt");StringBuilder stringBuilder=new StringBuilder();for(int i=0;i<list.size();i++){for(int j=0;j<list.get(i).size()-1;j++){double gap=Math.ceil((max[j]-min[j])/8);stringBuilder.append(Math.round((list.get(i).get(j)-min[j])/gap)).append(',');}stringBuilder.append(list1.get(i));stringBuilder.append("\n");}writeTxt(stringBuilder.toString());}
}