add hmm

Author: unknown

hmm/hmm.py

@@ -0,0 +1,238 @@
+# encoding=utf8
+
+import numpy as np
+import csv
+
+class HMM(object):
+    def __init__(self,N,M):
+        self.A = np.zeros((N,N))        # 状态转移概率矩阵
+        self.B = np.zeros((N,M))        # 观测概率矩阵
+        self.Pi = np.array([1.0/N]*N)   # 初始状态概率矩阵
+
+        self.N = N                      # 可能的状态数
+        self.M = M                      # 可能的观测数
+
+    def cal_probality(self, O):
+        self.T = len(O)
+        self.O = O
+
+        self.forward()
+        return sum(self.alpha[self.T-1])
+
+    def forward(self):
+        """
+        前向算法
+        """
+        self.alpha = np.zeros((self.T,self.N))
+
+        # 公式 10.15
+        for i in range(self.N):
+            self.alpha[0][i] = self.Pi[i]*self.B[i][self.O[0]]
+
+        # 公式10.16
+        for t in range(1,self.T):
+            for i in range(self.N):
+                sum = 0
+                for j in range(self.N):
+                    sum += self.alpha[t-1][j]*self.A[j][i]
+                self.alpha[t][i] = sum * self.B[i][self.O[t]]
+
+    def backward(self):
+        """
+        后向算法
+        """
+        self.beta = np.zeros((self.T,self.N))
+
+        # 公式10.19
+        for i in range(self.N):
+            self.beta[self.T-1][i] = 1
+
+        # 公式10.20
+        for t in range(self.T-2,-1,-1):
+            for i in range(self.N):
+                for j in range(self.N):
+                    self.beta[t][i] += self.A[i][j]*self.B[j][self.O[t+1]]*self.beta[t+1][j]
+
+    def cal_gamma(self, i, t):
+        """
+        公式 10.24
+        """
+        numerator = self.alpha[t][i]*self.beta[t][i]
+        denominator = 0
+
+        for j in range(self.N):
+            denominator += self.alpha[t][j]*self.beta[t][j]
+
+        return numerator/denominator
+
+    def cal_ksi(self, i, j, t):
+        """
+        公式 10.26
+        """
+
+        numerator = self.alpha[t][i]*self.A[i][j]*self.B[j][self.O[t+1]]*self.beta[t+1][j]
+        denominator = 0
+
+        for i in range(self.N):
+            for j in range(self.N):
+                denominator += self.alpha[t][i]*self.A[i][j]*self.B[j][self.O[t+1]]*self.beta[t+1][j]
+
+        return numerator/denominator
+
+    def init(self):
+        """
+        随机生成 A，B，Pi
+        并保证每行相加等于 1
+        """
+        import random
+        for i in range(self.N):
+            randomlist = [random.randint(0,100) for t in range(self.N)]
+            Sum = sum(randomlist)
+            for j in range(self.N):
+                self.A[i][j] = randomlist[j]/Sum
+
+        for i in range(self.N):
+            randomlist = [random.randint(0,100) for t in range(self.M)]
+            Sum = sum(randomlist)
+            for j in range(self.M):
+                self.B[i][j] = randomlist[j]/Sum
+
+    def train(self, O, MaxSteps = 100):
+        self.T = len(O)
+        self.O = O
+
+        # 初始化
+        self.init()
+
+        step = 0
+        # 递推
+        while step<MaxSteps:
+            step+=1
+            print(step)
+            tmp_A = np.zeros((self.N,self.N))
+            tmp_B = np.zeros((self.N,self.M))
+            tmp_pi = np.array([0.0]*self.N)
+
+            self.forward()
+            self.backward()
+
+            # a_{ij}
+            for i in range(self.N):
+                for j in range(self.N):
+                    numerator=0.0
+                    denominator=0.0
+                    for t in range(self.T-1):
+                        numerator += self.cal_ksi(i,j,t)
+                        denominator += self.cal_gamma(i,t)
+                    tmp_A[i][j] = numerator/denominator
+
+            # b_{jk}
+            for j in range(self.N):
+                for k in range(self.M):
+                    numerator = 0.0
+                    denominator = 0.0
+                    for t in range(self.T):
+                        if k == self.O[t]:
+                            numerator += self.cal_gamma(j,t)
+                        denominator += self.cal_gamma(j,t)
+                    tmp_B[j][k] = numerator / denominator
+
+            # pi_i
+            for i in range(self.N):
+                tmp_pi[i] = self.cal_gamma(i,0)
+
+            self.A = tmp_A
+            self.B = tmp_B
+            self.Pi = tmp_pi
+
+    def generate(self, length):
+        import random
+        I = []
+
+        # start
+        ran = random.randint(0,1000)/1000.0
+        i = 0
+        while self.Pi[i]<ran or self.Pi[i]<0.0001:
+            ran -= self.Pi[i]
+            i += 1
+        I.append(i)
+
+        # 生成状态序列
+        for i in range(1,length):
+            last = I[-1]
+            ran = random.randint(0, 1000) / 1000.0
+            i = 0
+            while self.A[last][i] < ran or self.A[last][i]<0.0001:
+                ran -= self.A[last][i]
+                i += 1
+            I.append(i)
+
+        # 生成观测序列
+        Y = []
+        for i in range(length):
+            k = 0
+            ran = random.randint(0, 1000) / 1000.0
+            while self.B[I[i]][k] < ran or self.B[I[i]][k]<0.0001:
+                ran -= self.B[I[i]][k]
+                k += 1
+            Y.append(k)
+
+        return Y
+
+
+
+def triangle(length):
+    '''
+    三角波
+    '''
+    X = [i for i in range(length)]
+    Y = []
+
+    for x in X:
+        x = x % 6
+        if x <= 3:
+            Y.append(x)
+        else:
+            Y.append(6-x)
+    return X,Y
+
+def sin(length):
+    '''
+    三角波
+    '''
+    import math
+    X = [i for i in range(length)]
+    Y = []
+
+    for x in X:
+        x = x % 20
+        Y.append(int(math.sin((x*math.pi)/10)*50)+50)
+    return X,Y
+
+
+
+def show_data(x,y):
+    import matplotlib.pyplot as plt
+    plt.plot(x, y, 'g')
+    plt.show()
+
+    return y
+
+
+if __name__ == '__main__':
+    hmm = HMM(10,4)
+    tri_x, tri_y = triangle(20)
+    
+    hmm.train(tri_y)
+    y = hmm.generate(100)
+    x = [i for i in range(100)]
+    show_data(x,y)
+
+    # hmm = HMM(15,101)
+    # sin_x, sin_y = sin(40)
+    # show_data(sin_x, sin_y)
+    # hmm.train(sin_y)
+    # y = hmm.generate(100)
+    # x = [i for i in range(100)]
+    # show_data(x,y)
+