HMM算法之维特比算法

参考李航《统计学习基础的》的公式推导

PI = np.array([0.2, 0.4, 0.4])
A = np.array([[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]])
B = np.array([[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]])
O = [1, 2, 1] # 观测序列



def viterbi(PI, A, B, O):  # 维特比算法
    T = len(O)  # 观测序列的数目
    N = len(PI)  # 所有可能的状态个数
    deta = PI * B[:, O[0] - 1]  # 初始
    pusai = np.zeros((T, N))
    seq = np.zeros(T) # 最优状态序列
    print deta, pusai[0]
    for t in range(1, T):
        tmp = [(deta * A[:, i]).tolist() for i in range(3)]
        pusai[t] = np.argmax(tmp, axis=1).tolist()
        deta = [max(deta * A[:, i]) for i in range(N)] * B[:, O[t] - 1]
        print deta, pusai[t]
    i = np.argmax(deta)  # 从最后一个开始回溯
    seq[-1] = int(i)
    pusai = np.mat(pusai)
    for t in range(T - 1, 0, -1):
        i = pusai[t, i]
        seq[t - 1] = i
    return seq