06 隐马尔可夫模型 - 案例二 - GMHMM应用

05 隐马尔可夫模型 - 案例一 - hmmlearn框架说明

常规操作

import numpy as np
from hmmlearn import hmm
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from sklearn.metrics.pairwise import pairwise_distances_argmin
import warnings

# 设置在jupyter中matplotlib的显示情况（默认inline是内嵌显示，通过设置为tk表示不内嵌显示）
%matplotlib tk

def expand(a, b):
    return 1.05*a-0.05*b, 1.05*b-0.05*a

warnings.filterwarnings("ignore")   # hmmlearn(0.2.0) < sklearn(0.18)

np.random.seed(28)
n = 5   # 隐状态数目
n_samples = 500 # 样本数量

pi = np.random.rand(n)
pi /= pi.sum()
print('初始概率：')
print(pi)

初始概率：
[ 0.28102534 0.21635059 0.04817319 0.1532667 0.30118418]

A = np.random.rand(n, n)
mask = np.zeros((n, n), dtype=np.bool)
mask[0][1] = mask[0][4] = True
mask[1][0] = mask[1][2] = True
mask[2][1] = mask[2][3] = True
mask[3][2] = mask[3][4] = True
mask[4][0] = mask[4][3] = True
A[mask] = 0
for i in range(n):
    A[i] /= A[i].sum()
print('转移概率:')
print(A)

转移概率:
[[ 0.2202672 0. 0.36791287 0.41181993 0. ]
[ 0. 0.4995834 0. 0.01356202 0.48685458]
[ 0.57655791 0. 0.10400763 0. 0.31943446]
[ 0.23695178 0.33043766 0. 0.43261056 0. ]
[ 0. 0.58044648 0.15883558 0. 0.26071794]]

# 给定均值
means = np.array(((30, 30, 30), (0, 50, 20), (-25, 30, 10),
   (-15, 0, 25), (15, 0, 40)), dtype=np.float)
for i in range(n):
    means[i,:] /= np.sqrt(np.sum(means ** 2, axis=1))[i]
print('均值：')
print(means)

均值：
[[ 0.57735027 0.57735027 0.57735027]
[ 0. 0.92847669 0.37139068]
[-0.62017367 0.74420841 0.24806947]
[-0.51449576 0. 0.85749293]
[ 0.35112344 0. 0.93632918]]

# 给定方差
covars = np.empty((n, 3, 3))
for i in range(n):
    covars[i] = np.diag(np.random.rand(3)*0.02+0.001)    # np.random.rand ∈[0,1)
print('方差：\n')
print(covars)

方差：
[[[ 0.0155071 0. 0. ]
[ 0. 0.02010293 0. ]
[ 0. 0. 0.00246192]]

[[ 0.00994326 0. 0. ]
[ 0. 0.01782236 0. ]
[ 0. 0. 0.00391079]]

[[ 0.01630543 0. 0. ]
[ 0. 0.0166357 0. ]
[ 0. 0. 0.01450157]]

[[ 0.00363404 0. 0. ]
[ 0. 0.00178606 0. ]
[ 0. 0. 0.01412046]]

[[ 0.00602365 0. 0. ]
[ 0. 0.02076837 0. ]
[ 0. 0. 0.01166766]]]

---

产生对应的模拟数据

model = hmm.GaussianHMM(n_components=n, covariance_type='full')
model.startprob_ = pi
model.transmat_ = A
model.means_ = means
model.covars_ = covars
sample, labels = model.sample(n_samples=n_samples, random_state=0)

模型构建及估计参数

model = hmm.GaussianHMM(n_components=n, n_iter=10)
model.fit(sample)
y = model.predict(sample)
np.set_printoptions(suppress=True)
print('##估计初始概率：')
print(model.startprob_)
print('##估计转移概率：')
print(model.transmat_)
print('##估计均值：\n')
print(model.means_)
print('##估计方差：\n')
print(model.covars_)

估计初始概率：
[ 0. 0. 1. 0. 0.]

估计转移概率：
[[ 0.53070513 0.4517509 0.01754397 0. 0. ]
[ 0.61038015 0.22727271 0. 0.16234714 0. ]
[ 0.31707317 0. 0.48780488 0. 0.19512195]
[ 0. 0.39536948 0. 0.11627515 0.48835537]
[ 0. 0. 0.48484864 0.39393919 0.12121216]]

估计均值：
[[-0.00362689 0.92283254 0.37226357]
[ 0.34487731 -0.0019567 0.93881756]
[-0.5168573 0.00094903 0.85695108]
[-0.66622524 0.72555611 0.24211216]
[ 0.5569746 0.62964009 0.56671171]]

估计方差：
[[[ 0.00893011 0. 0. ]
[ 0. 0.01465261 0. ]
[ 0. 0. 0.00340065]]

[[ 0.00580409 0. 0. ]
[ 0. 0.0202683 0. ]
[ 0. 0. 0.01309222]]

[[ 0.00341816 0. 0. ]
[ 0. 0.00196013 0. ]
[ 0. 0. 0.01525896]]

[[ 0.0167428 0. 0. ]
[ 0. 0.01308771 0. ]
[ 0. 0. 0.01618956]]

[[ 0.01625934 0. 0. ]
[ 0. 0.01590626 0. ]
[ 0. 0. 0.00207361]]]

---

根据类别信息更改顺序

order = pairwise_distances_argmin(means, model.means_, metric='euclidean')
print(order)
pi_hat = model.startprob_[order]
A_hat = model.transmat_[order]
A_hat = A_hat[:, order]
means_hat = model.means_[order]
covars_hat = model.covars_[order]
change = np.empty((n, n_samples), dtype=np.bool)
for i in range(n):
    change[i] = y == order[i]
for i in range(n):
    y[change[i]] = i
print('估计初始概率：')
print(pi_hat)
print('估计转移概率：')
print(A_hat)
print('估计均值：')
print(means_hat)
print('估计方差：')
print(covars_hat)
print(labels)
print(y)
acc = np.mean(labels == y) * 100
print('准确率：%.2f%%' % acc)

[4 0 3 2 1]
估计初始概率：
[ 0. 0. 0. 1. 0.]
估计转移概率：
[[ 0.12121216 0. 0.39393919 0.48484864 0. ]
[ 0. 0.53070513 0. 0.01754397 0.4517509 ]
[ 0.48835537 0. 0.11627515 0. 0.39536948]
[ 0.19512195 0.31707317 0. 0.48780488 0. ]
[ 0. 0.61038015 0.16234714 0. 0.22727271]]
估计均值：
[[ 0.5569746 0.62964009 0.56671171]
[-0.00362689 0.92283254 0.37226357]
[-0.66622524 0.72555611 0.24211216]
[-0.5168573 0.00094903 0.85695108]
[ 0.34487731 -0.0019567 0.93881756]]
估计方差：
[[[ 0.01625934 0. 0. ]
[ 0. 0.01590626 0. ]
[ 0. 0. 0.00207361]]

[[ 0.00893011 0. 0. ]
[ 0. 0.01465261 0. ]
[ 0. 0. 0.00340065]]

[[ 0.0167428 0. 0. ]
[ 0. 0.01308771 0. ]
[ 0. 0. 0.01618956]]

[[ 0.00341816 0. 0. ]
[ 0. 0.00196013 0. ]
[ 0. 0. 0.01525896]]

[[ 0.00580409 0. 0. ]
[ 0. 0.0202683 0. ]
[ 0. 0. 0.01309222]]]
[3 3 3 3 3 3 1 4 4 1 1 1 4 1 1 4 1 4 1 4 1 4 2 4 4 2 4 1 4 2 2 4 1 4 1 4 1
1 4 1 1 4 1 4 1 4 1 1 4 2 4 1 4 2 0 2 4 4 2 0 2 0 0 2 0 3 0 2 0 2 2 4 1 1
4 2 4 1 4 1 1 4 1 1 1 1 4 2 0 3 3 0 2 0 3 3 0 3 3 1 1 1 1 4 1 1 1 1 4 2 0
2 0 0 2 4 1 1 4 4 2 0 2 2 2 0 3 3 1 1 1 1 1 1 1 4 1 4 1 4 1 1 4 1 4 4 1 4
1 4 1 1 4 1 4 4 4 1 4 1 1 4 1 4 1 1 4 2 0 2 4 1 4 4 4 1 1 1 4 4 1 4 4 1 1
4 1 1 1 4 1 1 1 4 1 4 4 1 4 1 1 1 1 4 1 1 1 4 4 1 1 1 1 4 4 1 1 1 1 4 1 1
1 4 4 1 1 1 4 2 2 4 1 3 0 3 0 3 3 3 3 1 4 4 1 4 1 3 3 3 0 0 3 1 4 1 4 1 4
4 4 4 1 4 4 4 4 1 4 1 4 1 4 1 1 1 4 1 4 4 1 1 3 1 1 1 4 1 1 1 1 4 4 2 4 1
4 4 1 4 1 4 1 4 1 1 4 1 4 4 1 4 2 0 3 3 0 3 1 1 1 4 2 0 2 4 2 0 3 3 3 3 3
1 4 1 4 1 1 1 1 1 1 1 1 4 1 1 1 4 4 1 1 4 1 1 4 1 1 1 1 1 4 1 1 4 1 4 4 4
1 1 1 1 4 1 1 4 1 4 1 1 1 4 2 0 3 1 1 1 1 1 1 4 2 4 1 4 1 1 1 1 1 1 1 1 4
1 1 1 1 1 4 4 4 2 4 1 4 1 1 1 1 1 1 1 1 4 1 4 1 1 1 4 2 0 3 1 1 1 4 1 1 1
4 2 4 4 1 4 2 0 3 3 1 1 4 4 4 4 2 0 2 0 2 4 1 1 1 4 2 0 3 1 4 1 3 0 0 3 1
1 1 4 1 1 4 1 1 1 1 4 2 4 1 4 1 4 1 4]
[3 3 3 3 3 3 1 4 4 1 1 1 4 1 1 4 1 4 1 4 1 4 2 4 4 2 4 1 4 2 2 4 1 4 1 4 1
1 4 1 1 4 1 4 1 4 1 1 4 2 4 1 4 2 0 2 4 4 2 0 2 0 0 2 0 3 0 2 0 2 2 4 1 1
4 2 4 1 4 1 1 4 1 1 1 1 4 2 0 3 3 0 2 0 3 3 0 3 3 1 1 1 1 4 1 1 1 1 4 2 0
2 0 0 2 4 1 1 4 4 2 0 2 2 2 0 3 3 1 1 1 1 1 1 1 4 1 4 1 4 1 1 4 1 4 4 1 4
1 4 1 1 4 1 4 4 4 1 4 1 1 4 1 4 1 1 4 2 0 2 4 1 4 4 4 1 1 1 4 4 1 4 4 1 1
4 1 1 1 4 1 1 1 4 1 4 4 1 4 1 1 1 1 4 1 1 1 4 4 1 1 1 1 4 4 1 1 1 1 4 1 1
1 4 4 1 1 1 4 2 2 4 1 3 0 3 0 3 3 3 3 1 4 4 1 4 1 3 3 3 0 0 3 1 4 1 4 1 4
4 4 4 1 4 4 4 4 1 4 1 4 1 4 1 1 1 4 1 4 4 1 1 3 1 1 1 4 1 1 1 1 4 4 2 4 1
4 4 1 4 1 4 1 4 1 1 4 1 4 4 1 4 2 0 3 3 0 3 1 1 1 4 2 0 2 4 2 0 3 3 3 3 3
1 4 1 4 1 1 1 1 1 1 1 1 4 1 1 1 4 4 1 1 4 1 1 4 1 1 1 1 1 4 1 1 4 1 4 4 4
1 1 1 1 4 1 1 4 1 4 1 1 1 4 2 0 3 1 1 1 1 1 1 4 2 4 1 4 1 1 1 1 1 1 1 1 4
1 1 1 1 1 4 4 4 2 4 1 4 1 1 1 1 1 1 1 1 4 1 4 1 1 1 4 2 0 3 1 1 1 4 1 1 1
4 2 4 4 1 4 2 0 3 3 1 1 4 4 4 4 2 0 2 0 2 4 1 1 1 4 2 0 3 1 4 1 3 0 0 3 1
1 1 4 1 1 4 1 1 1 1 4 2 4 1 4 1 4 1 4]
准确率：100.00%

---

画图

mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False
fig = plt.figure(figsize=(8, 8), facecolor='w')
ax = fig.add_subplot(111, projection='3d')
colors = plt.cm.Spectral(np.linspace(0,1,n))
ax.scatter(sample[:, 0], sample[:, 1], sample[:, 2], s=50, c=labels, 
      cmap=plt.cm.Spectral, marker='o', label=u'观测值', depthshade=True)
plt.plot(sample[:, 0], sample[:, 1], sample[:, 2], lw=0.1, color='#A07070')
colors = plt.cm.Spectral(np.linspace(0, 1, n))
ax.scatter(means[:, 0], means[:, 1], means[:, 2], s=300, c=colors, 
      edgecolor='r', linewidths=1, marker='*', label=u'中心')

x_min, y_min, z_min = sample.min(axis=0)
x_max, y_max, z_max = sample.max(axis=0)
x_min, x_max = expand(x_min, x_max)
y_min, y_max = expand(y_min, y_max)
z_min, z_max = expand(z_min, z_max)
ax.set_xlim((x_min, x_max))
ax.set_ylim((y_min, y_max))
ax.set_zlim((z_min, z_max))
plt.legend(loc='upper left')
plt.grid(True)
plt.tight_layout(1)
plt.title(u'GMHMM参数估计和类别判定', fontsize=18)
plt.show()

07 隐马尔可夫模型 - 案例三 - 股票数据维度信息提取