import numpy as np
from sklearn.linear_model import LinearRegression, RidgeCV
from sklearn.preprocessing import PolynomialFeatures
import matplotlib.pyplot as plt
from sklearn.pipeline import Pipeline
import matplotlib as mpl
if __name__ == "__main__":
np.random.seed(0)
N = 9
x = np.linspace(0, 6, N) + np.random.randn(N)
x = np.sort(x)
y = x**2 - 4*x - 3 + np.random.randn(N)
x.shape = -1, 1
y.shape = -1, 1
model_1 = Pipeline([
('poly', PolynomialFeatures()),
('linear', LinearRegression(fit_intercept=False))])
model_2 = Pipeline([
('poly', PolynomialFeatures()),
('linear', RidgeCV(alphas=np.logspace(-3, 2, 100), fit_intercept=False))])
models = model_1, model_2
mpl.rcParams['font.sans-serif'] = [u'simHei']
mpl.rcParams['axes.unicode_minus'] = False
np.set_printoptions(suppress=True)
plt.figure(figsize=(9, 11), facecolor='w')
d_pool = np.arange(1, N, 1) # 阶
m = d_pool.size
clrs = [] # 颜色
for c in np.linspace(16711680, 255, m):
clrs.append('%d' % c)
line_width = np.linspace(5, 2, m)
titles = u'线性回归', u'Ridge回归'
for t in range(2):
model = models[t]
plt.subplot(2, 1, t+1)
plt.plot(x, y, 'ro', ms=10, zorder=N)
for i, d in enumerate(d_pool):
model.set_params(poly__degree=d)
model.fit(x, y)
lin = model.get_params('linear')['linear']
if t == 0:
print(u'%d阶,系数为:' % d, lin.coef_.ravel())
else:
print(u'%d阶,alpha=%.6f,系数为:' % (d, lin.alpha_), lin.coef_.ravel())
x_hat = np.linspace(x.min(), x.max(), num=100)
x_hat.shape = -1, 1
y_hat = model.predict(x_hat)
s = model.score(x, y)
print(s, '\n')
zorder = N - 1 if (d == 2) else 0
plt.plot(x_hat, y_hat, color=clrs[i], lw=line_width[i], label=(u'%d阶,score=%.3f' % (d, s)), zorder=zorder)
plt.legend(loc='upper left')
plt.grid(True)
plt.title(titles[t], fontsize=16)
plt.xlabel('X', fontsize=14)
plt.ylabel('Y', fontsize=14)
plt.tight_layout(1, rect=(0, 0, 1, 0.95))
plt.suptitle(u'多项式曲线拟合', fontsize=18)
plt.show()
用线性回归进行多项式拟合
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转载自blog.csdn.net/weixin_38241876/article/details/84857681
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