HMM算法之维特比算法

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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

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