def stand_regres(dataset,label):"""标准线性回归函数dataset:listlabel:list"""X = np.mat(dataset)Y = np.mat(label).Ttemp = X.T * Xif np.linalg.det(temp) == 0.0:  #计算行式的值print("X.T*X没有逆矩阵")return else:temp = temp.I * X.T * Yreturn temp

def plot_stand_regress(dataset,label,ws,ax):"""绘制数据集和拟合曲线"""dataset_matrix = np.mat(dataset)x = dataset_matrix[:,1]y = labelcal_y = dataset * wsax.scatter(x.T.getA(),y,s=10,c='red')ax.plot(x,cal_y)

print(np.corrcoef(cal_y.T,np.mat(y)))

def lwrw(test_point, xarray, yarray, k = 1.0):"""局部加权回归函数(locally weighted linear regression)dataset:listlabel:list"""mat_x = np.mat(xarray)mat_y = np.mat(yarray).Trow,col = np.shape(mat_x)    weights = np.mat(np.eye(row))for i in range(row):diffmat = test_point - mat_x[i,:]weights[i,i] = np.exp((diffmat*diffmat.T)/(-2.0*k*k))temp = mat_x.T * weights * mat_xif np.linalg.det(temp) == 0.0:print("mat_x.T * weights * X没有逆矩阵")return else:temp = temp.I * mat_x.T * weights * mat_yreturn test_point*temp

def plot_lwrw_regress(dataset,label,cal_y_list,ax):"""绘制数据集和拟合曲线"""dataset_matrix = np.mat(dataset)x = dataset_matrix[:,1]y = labelax.scatter(x.T.getA(),y,s=10,c='red')#对dataset进行排序sorted_index = x.argsort(0)sorted_x = dataset_matrix[sorted_index][:,0,:] #关键ax.plot(sorted_x[:,1],cal_y_list[sorted_index])if __name__ == "__main__":dataset,label = load_dataset('dataset/ex0.txt')fig = plt.figure()#当k为0.01时for row in range(rows):cal_y = lwrw(dataset[row],dataset,label,0.01)x_y_map[row] = cal_yax = fig.add_subplot(323)ax.text(0.05,4.2,'k=0.01')plot_lwrw_regress(dataset,label,x_y_map,ax)#当k为0.003for row in range(rows):cal_y = lwrw(dataset[row],dataset,label,0.003)x_y_map[row] = cal_yax = fig.add_subplot(325)ax.text(0.05,4.2,'k=0.003')plot_lwrw_regress(dataset,label,x_y_map,ax)plt.show()

def ridge_regres(xarray,yarray,lam=0.2):"""岭回归处理当特征比样本点还多，也酒水说输入数据的矩阵X不是满秩矩阵，非满秩矩阵在求逆时会出现问题w = (X.T*X + rI).I * X.T * Y"""xmat = np.mat(xarray)ymat = np.mat(yarray).Txtx = xmat.T * xmatdenom = xtx + np.eye(np.shape(xmat)[1])*lamif np.linalg.det(denom) == 0.0:print('denom 没有逆矩阵')ws = denom.I * xmat.T * ymatreturn wsdef ridge_test(xarray,yarray,ax):xmat = np.mat(xarray)row,col = np.shape(xmat)ymat = np.mat(yarray)xmean,xvar = data_normalize(xarray) #对数据进行标准化处理np.seterr(divide='ignore',invalid='ignore')xmat = (xmat - xmean) / xvarnum_test_pts = 30wmat = np.ones((num_test_pts,col))lam_list = []for i in range(num_test_pts):lam = np.exp(i-10)lam_list.append(i-10)ws = ridge_regres(xarray,yarray,lam)wmat[i,:] = ws.T#绘制不同lam情况下参数变化情况for j in range(np.shape(wmat)[1]):ax.plot(lam_list,wmat[:,j])

数据标准化，使其分布满足0均值和单位方差
在每轮迭代过程中：设置当前最小误差lowestError为正无穷对每个特征：增大或减少：改变一个系数得到一个新的w计算新w下的误差如果误差error小于当前最小误差：设置wbest等于当前的w将当前w设置为新的wbest

def stage_wise(dataset,label,step,numiter=100):"""前向逐步回归"""xmat = np.mat(dataset)xmean,xvar = data_normalize(dataset) #平均值和标准差ymat = np.mat(label).Tymat = ymat - np.mean(ymat,0)xmat = (xmat - xmean) / xvarm,n = np.shape(xmat)return_mat = np.zeros((numiter,n))ws = np.zeros((n,1))ws_test = ws.copy()ws_max = ws.copy()for iter in range(numiter):  #迭代次数lowest_error = np.inffor j in range(n):  #对每个特征进行变量for sign in [-1,1]:ws_test = ws.copy()ws_test[j] += step*signytest = xmat * ws_testrssE = ((ymat.A-ytest.A)**2).sum()if rssE < lowest_error:lowest_error = rssEws_max = ws_testws = ws_max.copy()return_mat[iter,:] = ws.Treturn return_mat    def stage_wise_test(ws_mat,iternum,ax):"""前向逐步回归算法中回归系数随迭代次数的变化情况"""    x = range(iternum)for i in range(np.shape(ws_mat)[1]):ax.plot(x,ws_mat[:,i])

#前向逐步回归
ax = fig.add_subplot(326)
ws = stage_wise(dataset,label,0.01,500)
print("前向逐步回归经过迭代后的最后回归系数：",ws[-1,:])
stage_wise_test(ws,500,ax)

    #使用标准回归对"dataset/abalone.txt"数据集进行测试#对数据进行标准化处理xman,xvar = data_normalize(dataset)xmat = np.mat(dataset)xmat = (xmat - xman) / xvarymat = np.mat(label)ax = stand_regres(xmat,ymat)print("标准回归后得到的回归系数：",ws[-1,:])