本題純粹用作練習(xí)，無(wú)任何其他意義。

采用高斯基函數(shù)作為線(xiàn)性回歸模型，用sklearn.gaussian_process.GaussianProcessRegressor可以進(jìn)行回歸，順便學(xué)習(xí)畫(huà)3D圖。

代碼如下：

# -*- coding: utf-8 -*- import numpy as np import matplotlib.pyplot as plt from sklearn.gaussian_process import GaussianProcessRegressor from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C from mpl_toolkits.mplot3d import Axes3Dtest = np.array([[2004,98.31]]) data = np.array([[2001,100.83,410],[2005,90.9,500],[2007,130.03,550],[2004,78.88,410],[2006,74.22,460],[2005,90.4,497],[1983,64.59,370],[2000,164.06,610],[2003,147.5,560],[2003,58.51,408],[1999,95.11,565],[2000,85.57,430],[1995,66.44,378],[2003,94.27,498],[2007,125.1,760],[2006,111.2,730],[2008,88.99,430],[2005,92.13,506],[2008,101.35,405],[2000,158.9,615]]) kernel = C(0.1, (0.001,0.1))*RBF(0.5,(1e-4,10)) reg = GaussianProcessRegressor(kernel=kernel,n_restarts_optimizer=10,alpha=0.1) reg.fit(data[:,:-1], data[:,-1]) x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1 y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1 xset, yset = np.meshgrid(np.arange(x_min, x_max, 0.5), np.arange(y_min, y_max, 0.5)) output,err = reg.predict(np.c_[xset.ravel(), yset.ravel()],return_std=True) output,err = output.reshape(xset.shape),err.reshape(xset.shape) sigma = np.sum(reg.predict(data[:,:-1], return_std=True)[1]) up,down = output*(1+1.96*err), output*(1-1.96*err)fig = plt.figure(figsize=(10.5,5)) ax1 = fig.add_subplot(121, projection='3d') surf = ax1.plot_wireframe(xset,yset,output, rstride=10, cstride=2, antialiased=True) surf_u = ax1.plot_wireframe(xset,yset,up,colors='lightgreen',linewidths=1,rstride=10, cstride=2, antialiased=True) surf_d = ax1.plot_wireframe(xset,yset,down,colors='lightgreen',linewidths=1,rstride=10, cstride=2, antialiased=True) ax1.scatter(data[:,0],data[:,1],data[:,2],c='red') ax1.set_title('House Price at (2004, 98.31): {0:.2f}$*10^4$ RMB'.format(reg.predict(test)[0])) ax1.set_xlabel('Year') ax1.set_ylabel('Area, $m^2$') ax1.set_zlabel('Price,$10^4$ RMB')ax = fig.add_subplot(122) s = ax.scatter(data[:,0],data[:,1],c=data[:,2],cmap=plt.cm.viridis) # ax.contour(xset,yset,output) im = ax.imshow(output, interpolation='bilinear', origin='lower',extent=(x_min, x_max-1, y_min, y_max), aspect='auto') plt.colorbar(s,ax=ax) ax.set_title('House Price,$10^4$ RMB') ax.hlines(test[0,1],x_min, x_max-1) ax.vlines(test[0,0],y_min, y_max) ax.text(test[0,0],test[0,1],'{0:.2f}$*10^4$ RMB'.format(reg.predict(test)[0]),ha='left',va='bottom',color='k',size=11,rotation=90) ax.set_xlabel('Year') ax.set_ylabel('Area, $m^2$') plt.subplots_adjust(left=0.05, top=0.95, right=0.95) plt.show()成圖如下：（左圖中綠色網(wǎng)格面為置信度為95%的上下界面，藍(lán)色網(wǎng)格為回歸面）

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