线性回归

Author: lawlite19

LinearRegression/LinearRegression.py

@@ -0,0 +1,111 @@
+import numpy as np
+from matplotlib import pyplot as plt
+
+
+def linearRegression(alpha=0.01,num_iters=400):
+    print "加载数据...\n"
+    
+    data = loadtxtAndcsv_data("data.txt",",",np.float64)  #读取数据
+    X = data[:,0:-1]      # X对应0到倒数第2列                  
+    y = data[:,-1]        # y对应最后一列  
+    m = len(y)            # 总的数据条数
+    col = data.shape[1]      # data的列数
+    
+    X,mu,sigma = featureNormaliza(X)    # 归一化
+    plot_X1_X2(X)         # 画图看一下归一化效果
+    
+    X = np.hstack((np.ones((m,1)),X))    # 在X前加一列1
+    
+    print "\n执行梯度下降算法....\n"
+    
+    theta = np.zeros((col,1))
+    y = y.reshape(-1,1)   #将行向量转化为列
+    theta,J_history = gradientDescent(X, y, theta, alpha, num_iters)
+    
+    plotJ(J_history, num_iters)
+    
+    return mu,sigma,theta   #返回均值mu,标准差sigma,和学习的结果theta
+    
+   
+# 加载txt和csv文件
+def loadtxtAndcsv_data(fileName,split,dataType):
+    return np.loadtxt(fileName,delimiter=split,dtype=dataType)
+
+# 加载npy文件
+def loadnpy_data(fileName):
+    return np.load(fileName)
+
+# 归一化feature
+def featureNormaliza(X):
+    X_norm = np.array(X)            #将X转化为numpy数组对象，才可以进行矩阵的运算
+    #定义所需变量
+    mu = np.zeros((1,X.shape[1]))   
+    sigma = np.zeros((1,X.shape[1]))
+    
+    mu = np.mean(X_norm,0)          # 求每一列的平均值（0指定为列，1代表行）
+    sigma = np.std(X_norm,0)        # 求每一列的标准差
+    for i in range(X.shape[1]):     # 遍历列
+        X_norm[:,i] = (X_norm[:,i]-mu[i])/sigma[i]  # 归一化
+    
+    return X_norm,mu,sigma
+
+# 画二维图
+def plot_X1_X2(X):
+    plt.scatter(X[:,0],X[:,1])
+    plt.show()
+
+
+# 梯度下降算法
+def gradientDescent(X,y,theta,alpha,num_iters):
+    m = len(y)      
+    n = len(theta)
+    
+    temp = np.matrix(np.zeros((n,num_iters)))   # 暂存每次迭代计算的theta，转化为矩阵形式
+    
+    
+    J_history = np.zeros((num_iters,1)) #记录每次迭代计算的代价值
+    
+    for i in range(num_iters):  # 遍历迭代次数    
+        h = np.dot(X,theta)     # 计算内积，matrix可以直接乘
+        temp[:,i] = theta - ((alpha/m)*(np.dot(np.transpose(X),h-y)))   #梯度的计算
+        theta = temp[:,i]
+        J_history[i] = computerCost(X,y,theta)      #调用计算代价函数
+        print '.',      
+    return theta,J_history  
+
+# 计算代价函数
+def computerCost(X,y,theta):
+    m = len(y)
+    J = 0
+    
+    J = (np.transpose(X*theta-y))*(X*theta-y)/(2*m) #计算代价J
+    return J
+
+# 画每次迭代代价的变化图
+def plotJ(J_history,num_iters):
+    x = np.arange(1,num_iters+1)
+    plt.plot(x,J_history)
+    plt.xlabel("num_iters")
+    plt.ylabel("J")
+    plt.show()
+
+# 测试linearRegression函数
+def testLinearRegression():
+    mu,sigma,theta = linearRegression(0.01,400)
+    print "\n计算的theta值为：\n",theta
+    print "\n预测结果为：%f"%predict(mu, sigma, theta)
+    
+# 测试学习效果（预测）
+def predict(mu,sigma,theta):
+    result = 0
+    # 注意归一化
+    predict = np.array([1650,3])
+    norm_predict = (predict-mu)/sigma
+    final_predict = np.hstack((np.ones((1)),norm_predict))
+    
+    result = np.dot(final_predict,theta)    # 预测结果
+    return result
+    
+    
+if __name__ == "__main__":
+    testLinearRegression()

LinearRegression/data.csv

@@ -0,0 +1,47 @@
+2104,3,399900
+1600,3,329900
+2400,3,369000
+1416,2,232000
+3000,4,539900
+1985,4,299900
+1534,3,314900
+1427,3,198999
+1380,3,212000
+1494,3,242500
+1940,4,239999
+2000,3,347000
+1890,3,329999
+4478,5,699900
+1268,3,259900
+2300,4,449900
+1320,2,299900
+1236,3,199900
+2609,4,499998
+3031,4,599000
+1767,3,252900
+1888,2,255000
+1604,3,242900
+1962,4,259900
+3890,3,573900
+1100,3,249900
+1458,3,464500
+2526,3,469000
+2200,3,475000
+2637,3,299900
+1839,2,349900
+1000,1,169900
+2040,4,314900
+3137,3,579900
+1811,4,285900
+1437,3,249900
+1239,3,229900
+2132,4,345000
+4215,4,549000
+2162,4,287000
+1664,2,368500
+2238,3,329900
+2567,4,314000
+1200,3,299000
+852,2,179900
+1852,4,299900
+1203,3,239500

LinearRegression/data.npy

@@ -0,0 +1,47 @@
+2104,3,399900
+1600,3,329900
+2400,3,369000
+1416,2,232000
+3000,4,539900
+1985,4,299900
+1534,3,314900
+1427,3,198999
+1380,3,212000
+1494,3,242500
+1940,4,239999
+2000,3,347000
+1890,3,329999
+4478,5,699900
+1268,3,259900
+2300,4,449900
+1320,2,299900
+1236,3,199900
+2609,4,499998
+3031,4,599000
+1767,3,252900
+1888,2,255000
+1604,3,242900
+1962,4,259900
+3890,3,573900
+1100,3,249900
+1458,3,464500
+2526,3,469000
+2200,3,475000
+2637,3,299900
+1839,2,349900
+1000,1,169900
+2040,4,314900
+3137,3,579900
+1811,4,285900
+1437,3,249900
+1239,3,229900
+2132,4,345000
+4215,4,549000
+2162,4,287000
+1664,2,368500
+2238,3,329900
+2567,4,314000
+1200,3,299000
+852,2,179900
+1852,4,299900
+1203,3,239500

LinearRegression/data.txt

@@ -0,0 +1,35 @@
+线性回归算法
+=======
+### 一、文件说明
+- [main.m][1.1]
+ - 主运行程序
+- [featureNormalize.m][1.2]
+ - 特征向量归一化函数
+- [gradientDescent.m][1.3]
+ - 梯度下降求解函数
+- [computerCost.m][1.4]
+ - 计算代价J函数
+- [normalEquations.m][1.5]
+ - 正规方程求解函数
+
+### 二、重要文件说明
+- main.m
+ - 注意合理修改学习速率参数`alpha`
+ - 归一化数据，预测时也需要归一化（因为是归一化之后求出的theta参数）
+
+### 三、测试数据
+- 代价函数随迭代次数收敛
+![线性回归][3.1]
+
+
+
+
+
+[1.1]:main.m
+[1.2]:featureNormalize.m
+[1.3]:gradientDescent.m
+[1.4]:computerCost.m
+[1.5]:normalEquations.m
+
+
+  [3.1]: ../images/LinearRegression_01.png "LinearRegression_01.png"