感知机算法的两种表示
感知机算法的原始形式
输入:训练数据集T={(x1,y1),(x2,y2),...,(xn,yn)},其中xi属于Rn(n维空间向量)，yi={-1,+1},i=1,2,...,N
学习率t（0<t<=1）;
输出：w,b;感知机模型f(x)=sign(w*x+b)
(1)选取初值w0,b0一般为 0
(2)在训练集中选取数据(xi,yi)
(3)如果yi(w*xi+b)<=0
w<---w+tyixi
b<----b+tyi
(4)转至（2）,直至训练集中没有误分类点。
算法代码如下
1 import java.util.Random; 2 import java.util.Scanner; 3 import java.util.regex.Matcher; 4 import java.util.regex.Pattern; 5 6 //初始的感知机学习算法 7 public class ganzhijiOriginal { 8 // 数据集中数据的个数 9 public static int NCount; 10 // 数据中每个数值的维数 不包含y 11 public static int N; 12 // 学习率 (0,1] 13 public static float t; 14 15 // 保存数据 16 public static int datas[][]; 17 // 权重向量 18 public static float w[]; 19 // 偏移数据 20 public static float b; 21 22 public static void main(String args[]) { 23 Scanner sca = new Scanner(System.in); 24 // 默认输入的格式为 N-t-b 25 System.out.println("输入格式为N-t-b-NCount的数据:"); 26 String lines = sca.nextLine(); 27 Pattern pattern = Pattern.compile("(.*)-(.*)-(.*)-(.*)"); 28 Matcher matcher = pattern.matcher(lines); 29 matcher.find(); 30 N = Integer.parseInt(matcher.group(1)); 31 t = Float.parseFloat(matcher.group(2)); 32 b = Float.parseFloat(matcher.group(3)); 33 // b = Integer.parseInt(matcher.group(3)); 34 NCount = Integer.parseInt(matcher.group(4)); 35 // System.out.println("请输入权重向量的初始值格式为格式为x,x,x,x" + N); 36 //初始化数据集 37 w = new float[N]; 38 // lines = sca.nextLine(); 39 // String[] str = lines.split(","); 40 // for (int i = 0; i < N; i++) 41 // w[i] = Float.parseFloat(str[i]); 42 datas = new int[NCount][N + 1]; 43 System.out.println("请输入所有权重向量的初始值"); 44 for (int i = 0; i < NCount; i++) { 45 String line = sca.nextLine(); 46 String strs[] = line.split(" "); 47 for (int j = 0; j <= N; j++) 48 datas[i][j] = Integer.parseInt(strs[j]); 49 } 50 CountTheTimes = 0; 51 Random ra = new Random(); 52 int chooseNumber = ra.nextInt(NCount); 53 CalcuteAndUpdatValue(0); 54 String strd = ""; 55 for (int i = 0; i < N; i++) 56 strd += w[i] + "*x" + i + "+ "; 57 System.out.println("F(x)=sign(" + strd + b + ")"); 58 } 59 60 public static int CountTheTimes; 61 62 private static void CalcuteAndUpdatValue(int chooseNumber) { 63 float f = isPOrN(chooseNumber); 64 boolean flages = f * datas[chooseNumber][N] > 0 ? true : false; 65 if (!flages) { 66 for (int j = 0; j < N; j++) //更新权重w的值 67 w[j] = w[j] + t * datas[chooseNumber][N] * datas[chooseNumber][j]; 68 b = b + t * datas[chooseNumber][N]; 69 70 CountTheTimes = 0;//初始化 71 } else { 72 CountTheTimes++; 73 chooseNumber = (chooseNumber + 1) % NCount; 74 } 75 if (CountTheTimes == NCount) return; 76 CalcuteAndUpdatValue(chooseNumber); 77 } 78 79 private static float isPOrN(int chooseNumber) { 80 float sum = 0; 81 for (int i = 0; i < N; i++) sum += datas[chooseNumber][i] * w[i]; 82 return sum + b; 83 } 84 85 }
感知机算法的对偶形式
输入：线性可分的数据集T={(x1,y1),(x2,y2),...,(xn,yn)}其中xi属于Rn(n维向量),yi属于{-1，+1}，i，2，。。。，N；学习率为t (0<t<=1)
输出a，b 感知机模型f(x)=sign(j从1 到 ajyjxj*x累加 +b) 其中a=(a1,a2,a3...,an)T
(1)a<---0,b<----0
(2)在训练数据集中选择(xi,yi)
(3)如果 yi(j从1 到 ajyjxj*xi累加 +b)<=0
ai<----ai+t
b<---b+tyi
(4)转至(2)直到没有误分类点
算法如下
import java.util.Random; import java.util.Scanner; //感知机算法的对偶形式 public class ganzhijiOudui { //存储数据的Gram矩阵 public static int gramMatrix[][]; // 存储初始点集合包括y public static int datas[][]; //感知机中的学习率(0,1] public static float t; // 存储某个点更新的次数nt public static float a[]; // 点的维度 不包含y public static int N; // 总点的数 public static int NCount; //偏移量 public static float b; public static int w[];//权重 public static void main(String args[]) { Scanner sca = new Scanner(System.in); System.out.println("输入的格式为:N-t-b-NCount"); String line = sca.nextLine(); String dt[] = line.split("-"); N = Integer.parseInt(dt[0]); t = Float.parseFloat(dt[1]); b = Float.parseFloat(dt[2]); NCount = Integer.parseInt(dt[3]); InitDatas(sca); } private static void InitDatas(Scanner sca) { datas = new int[NCount][N + 1]; gramMatrix = new int[NCount][NCount]; w = new int[N]; // 默认值为零 a = new float[NCount]; System.out.println("输入数据点集合格式为x x x ... Y"); for (int i = 0; i < NCount; i++) { String line = sca.nextLine(); String strs[] = line.split(" "); for (int j = 0; j <= N; j++) datas[i][j] = Integer.parseInt(strs[j]); } System.out.println("初始化Gram矩阵"); for (int i = 0; i < NCount; i++) { for (int j = 0; j < NCount; j++) { gramMatrix[i][j] = MultiplyTheDatas(i, j); } } // 记录总的循环次数 TotalTimes = 0; Random random = new Random(); int chooseNumber = random.nextInt(NCount); CalculateAndUpdatDatas(0); //更新 w for (int i = 0; i < N; i++) { int sum = 0; for (int j = 0; j < NCount; j++) sum += a[j] * datas[j][i]*datas[j][N]; w[i] = sum; } String strd = ""; for (int i = 0; i < N; i++) strd += w[i] + "*x" + i + "+ "; System.out.println("F(x)=sign(" + strd + b + ")"); } public static int TotalTimes = 0; private static void CalculateAndUpdatDatas(int chooseNumber) { float sum = CaluteTheFx(chooseNumber); boolean flages = sum * datas[chooseNumber][N] > 0 ? true : false; if (!flages) { TotalTimes = 0; a[chooseNumber] = a[chooseNumber] + t; b = b + t * datas[chooseNumber][N]; } else { TotalTimes++; chooseNumber = (chooseNumber + 1) % NCount; } if (TotalTimes == NCount) return; CalculateAndUpdatDatas(chooseNumber); } private static float CaluteTheFx(int chooseNumber) { float sum = 0; for (int i = 0; i <=N; i++) sum += a[i] * datas[i][N] * gramMatrix[i][chooseNumber]; return sum + b; } // 计算两个向量的乘积 private static int MultiplyTheDatas(int i, int j) { int sum = 0; for (int k = 0; k <N; k++) sum += datas[i][k] * datas[j][k]; return sum; } }
