test_lwr.py

# coding: utf-8
# linear_regression/test_lwr.py
import regression
import matplotlib.pyplot as plt
import matplotlib.ticker as mtick
import numpy as np

if __name__ == "__main__":
    srcX, y = regression.loadDataSet('data/lwr.txt');

    m,n = srcX.shape
    srcX = np.concatenate((srcX[:, 0], np.power(srcX[:, 0],2)), axis=1)
    # 特征缩放
    X = regression.standardize(srcX.copy())
    X = np.concatenate((np.ones((m,1)), X), axis=1)

    rate = 0.1
    maxLoop = 1000
    epsilon = 0.01

    predicateX = regression.standardize(np.matrix([[8, 64]]))

    predicateX = np.concatenate((np.ones((1,1)), predicateX), axis=1)

    result, t = regression.lwr(rate, maxLoop, epsilon, X, y, predicateX, 1)
    theta, errors, thetas = result

    result2, t = regression.lwr(rate, maxLoop, epsilon, X, y, predicateX, 0.1)
    theta2, errors2, thetas2 = result2


    # 打印特征点
    fittingFig = plt.figure()
    title = 'polynomial with bgd: rate=%.2f, maxLoop=%d, epsilon=%.3f'%(rate,maxLoop,epsilon)
    ax = fittingFig.add_subplot(111, title=title)
    trainingSet = ax.scatter(srcX[:, 0].flatten().A[0], y[:,0].flatten().A[0])

    print theta
    print theta2

    # 打印拟合曲线
    xx = np.linspace(1, 7, 50)
    xx2 = np.power(xx,2)
    yHat1 = []
    yHat2 = []
    for i in range(50):
        normalizedSize = (xx[i]-xx.mean())/xx.std(0)
        normalizedSize2 = (xx2[i]-xx2.mean())/xx2.std(0)
        x = np.matrix([[1,normalizedSize, normalizedSize2]])
        yHat1.append(regression.h(theta, x.T))
        yHat2.append(regression.h(theta2, x.T))
    fittingLine1, = ax.plot(xx, yHat1, color='g')
    fittingLine2, = ax.plot(xx, yHat2, color='r')

    ax.set_xlabel('temperature')
    ax.set_ylabel('yield')

    plt.legend([trainingSet, fittingLine1, fittingLine2], ['Training Set', r'LWR with $\tau$=1', r'LWR with $\tau$=0.1'])
    plt.show()

    # 打印误差曲线
    errorsFig = plt.figure()
    ax = errorsFig.add_subplot(111)
    ax.yaxis.set_major_formatter(mtick.FormatStrFormatter('%.2e'))

    ax.plot(range(len(errors)), errors)
    ax.set_xlabel('Number of iterations')
    ax.set_ylabel('Cost J')

    plt.show()