SVR回归_时间序列分析优缺点

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Jetbrains全家桶1年46，售后保障稳定

1.SVR时间序列预测

SVR可用于时间序列分析，但不是较好的选择。现在一般采用LSTM神经网络来处理时间序列数据

# SVR预测
# 也可用于时间序列分析（ARIMA也可用于时间序列分析）
import numpy as np
from sklearn import svm
import matplotlib.pyplot as plt
if __name__ == "__main__":
# 构造数据
N = 50
np.random.seed(0)
# 排序
x = np.sort(np.random.uniform(0, 6, N), axis=0)
y = 2*np.sin(x) + 0.1*np.random.randn(N)
x = x.reshape(-1, 1)
print('x =\n', x)
print('y =\n', y)
# 高斯核函数
print('SVR - RBF')
svr_rbf = svm.SVR(kernel='rbf', gamma=0.2, C=100)
svr_rbf.fit(x, y)
# 线性核函数
print('SVR - Linear')
svr_linear = svm.SVR(kernel='linear', C=100)
svr_linear.fit(x, y)
# 多项式核函数
print('SVR - Polynomial')
svr_poly = svm.SVR(kernel='poly', degree=3, C=100)
svr_poly.fit(x, y)
print('Fit OK.')
# 思考：系数1.1改成1.5
x_test = np.linspace(x.min(), 1.1*x.max(), 100).reshape(-1, 1)
y_rbf = svr_rbf.predict(x_test)
y_linear = svr_linear.predict(x_test)
y_poly = svr_poly.predict(x_test)
plt.figure(figsize=(9, 8), facecolor='w')
plt.plot(x_test, y_rbf, 'r-', linewidth=2, label='RBF Kernel')
plt.plot(x_test, y_linear, 'g-', linewidth=2, label='Linear Kernel')
plt.plot(x_test, y_poly, 'b-', linewidth=2, label='Polynomial Kernel')
plt.plot(x, y, 'mo', markersize=6)
plt.scatter(x[svr_rbf.support_], y[svr_rbf.support_], s=200, c='r', marker='*', label='RBF Support Vectors', zorder=10)
plt.legend(loc='lower left')
plt.title('SVR', fontsize=16)
plt.xlabel('X')
plt.ylabel('Y')
plt.grid(True)
plt.tight_layout(2)
plt.show()

Jetbrains全家桶1年46，售后保障稳定

2.SVR调参

# SVR调参
import numpy as np
from sklearn import svm
from sklearn.model_selection import GridSearchCV    # 0.17 grid_search
import matplotlib.pyplot as plt
if __name__ == "__main__":
N = 50
np.random.seed(0)
x = np.sort(np.random.uniform(0, 6, N), axis=0)
y = 2*np.sin(x) + 0.1*np.random.randn(N)
x = x.reshape(-1, 1)
print('x =\n', x)
print('y =\n', y)
model = svm.SVR(kernel='rbf')
# 0.01~100取100个数字
c_can = np.logspace(-2, 2, 10)
gamma_can = np.logspace(-2, 2, 10)
svr = GridSearchCV(model, param_grid={ 
'C': c_can, 'gamma': gamma_can}, cv=5)
svr.fit(x, y)
print('验证参数：\n', svr.best_params_)
x_test = np.linspace(x.min(), x.max(), 100).reshape(-1, 1)
y_hat = svr.predict(x_test)
sp = svr.best_estimator_.support_
plt.figure(facecolor='w')
plt.scatter(x[sp], y[sp], s=120, c='r', marker='*', label='Support Vectors', zorder=3)
plt.plot(x_test, y_hat, 'r-', linewidth=2, label='RBF Kernel')
plt.plot(x, y, 'go', markersize=5)
plt.legend(loc='upper right')
plt.title('SVR', fontsize=16)
plt.xlabel('X')
plt.ylabel('Y')
plt.grid(True)
plt.show()

3.SVR高斯核与过拟合

import numpy as np
from sklearn import svm
import matplotlib as mpl
import matplotlib.colors
import matplotlib.pyplot as plt
def extend(a, b):
big, small = 1.01, 0.01
return big*a-small*b, big*b-small*a
if __name__ == "__main__":
t = np.linspace(-5, 5, 6)
t1, t2 = np.meshgrid(t, t)
print(t1.ravel().shape)
# np.stack按给定输出轴连接数组
x1 = np.stack((t1.ravel(), t2.ravel()), axis=1)
print(x1.shape)
N = len(x1)
x2 = x1 + (1, 1)
# np.concatenate沿现有轴连接一系列数组
x = np.concatenate((x1, x2))
y = np.array([1]*N + [-1]*N)
clf = svm.SVC(C=0.1, kernel='rbf', gamma=5)
clf.fit(x, y)
y_hat = clf.predict(x)
print('准确率：%.1f%%' % (np.mean(y_hat == y) * 100))
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False
cm_light = mpl.colors.ListedColormap(['#77E0A0', '#FFA0A0'])
cm_dark = mpl.colors.ListedColormap(['g', 'r'])
x1_min, x1_max = extend(x[:, 0].min(), x[:, 0].max())  # 第0列的范围
x2_min, x2_max = extend(x[:, 1].min(), x[:, 1].max())  # 第1列的范围
x1, x2 = np.mgrid[x1_min:x1_max:300j, x2_min:x2_max:300j]  # 生成网格采样点
grid_test = np.stack((x1.flat, x2.flat), axis=1)  # 测试点
grid_hat = clf.predict(grid_test)
grid_hat.shape = x1.shape  # 使之与输入的形状相同
plt.figure(facecolor='w')
plt.pcolormesh(x1, x2, grid_hat, cmap=cm_light)
plt.scatter(x[:, 0], x[:, 1], s=60, c=y, marker='o', cmap=cm_dark)
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'SVM的RBF核与过拟合', fontsize=18)
plt.tight_layout(0.2)
plt.show()

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