机器学习之线性回归及python实现

python代码实现（数据集：http://download.csdn.net/download/vinsuan1993/10173129）：

import numpy as npimport pylabdef compute_error(b,m,data):    totalError = 0    #Two ways to implement this    #first way    # for i in range(0,len(data)):    #     x = data[i,0]    #     y = data[i,1]    #    #     totalError += (y-(m*x+b))**2    #second way    x = data[:,0]    y = data[:,1]    totalError = (y-m*x-b)**2    totalError = np.sum(totalError,axis=0)    return totalError/float(len(data))#梯度下降def optimizer(data,starting_b,starting_m,learning_rate,num_iter):    b = starting_b    m = starting_m    #迭代次数    for i in range(num_iter):        b,m =compute_gradient(b,m,data,learning_rate)        if i%100==0:            print('iter {0}:error={1}'.format(i,compute_error(b,m,data)))    return [b,m]def compute_gradient(b_current,m_current,data ,learning_rate):    N = float(len(data))    x = data[:,0]    y = data[:,1]    b_gradient = -(2/N)*(y-m_current*x-b_current)    b_gradient = np.sum(b_gradient,axis=0)    m_gradient = -(2/N)*x*(y-m_current*x-b_current)    m_gradient = np.sum(m_gradient,axis=0)        #update our b and m values using out partial derivations    new_b = b_current - (learning_rate * b_gradient)    new_m = m_current - (learning_rate * m_gradient)    #得到新的参数值    return [new_b,new_m]def plot_data(data,b,m):    #plottting    x = data[:,0]    y = data[:,1]    y_predict = m*x+b    pylab.plot(x,y,'o')    pylab.plot(x,y_predict,'k-')    pylab.show()def Linear_regression():    # get train data    data =np.loadtxt('data.csv',delimiter=',')    #define hyperparamters    #learning_rate is used for update gradient    #defint the number that will iteration    # define  y =mx+b    learning_rate = 0.001    initial_b =0.0    initial_m = 0.0    num_iter = 1000    #train model    #print b m error    print('initial variables:\n initial_b = {0}\n intial_m = {1}\n error of begin = {2} \n'.format(initial_b,initial_m,compute_error(initial_b,initial_m,data)))    #optimizing b and m    [b ,m] = optimizer(data,initial_b,initial_m,learning_rate,num_iter)    #print final b m error    print('final formula parmaters:\n b = {1}\n m={2}\n error of end = {3} \n'.format(num_iter,b,m,compute_error(b,m,data)))    #plot result    plot_data(data,b,m)if __name__ =='__main__':    Linear_regression()