Create linear_regression_train.py

Author: zhaozhiyong19890102

Chapter_7 LinearRegression/linear_regression_train.py

@@ -0,0 +1,143 @@
+# coding:UTF-8
+
+import numpy as np
+from math import pow
+
+def load_data(file_path):
+    '''导入数据
+    input:  file_path(string):训练数据
+    output: feature(mat):特征
+            label(mat):标签
+    '''
+    f = open(file_path)
+    feature = []
+    label = []
+    for line in f.readlines():
+        feature_tmp = []
+        lines = line.strip().split("\t")
+        feature_tmp.append(1)  # x0
+        for i in xrange(len(lines) - 1):
+            feature_tmp.append(float(lines[i]))
+        feature.append(feature_tmp)
+        label.append(float(lines[-1]))
+    f.close()
+    return np.mat(feature), np.mat(label).T
+
+def least_square(feature, label):
+    '''最小二乘法
+    input:  feature(mat):特征
+            label(mat):标签
+    output: w(mat):回归系数
+    '''
+    w = (feature.T * feature).I * feature.T * label
+    return w
+
+def first_derivativ(feature, label, w):
+    '''计算一阶导函数的值
+    input:  feature(mat):特征
+            label(mat):标签
+    output: g(mat):一阶导数值
+    '''
+    m, n = np.shape(feature)
+    g = np.mat(np.zeros((n, 1)))
+    for i in xrange(m):
+        err = label[i, 0] - feature[i, ] * w
+        for j in xrange(n):
+            g[j, ] -= err * feature[i, j]
+    return g     
+
+def second_derivative(feature):
+    '''计算二阶导函数的值
+    input:  feature(mat):特征
+    output: G(mat):二阶导数值
+    '''
+    m, n = np.shape(feature)
+    G = np.mat(np.zeros((n, n)))
+    for i in xrange(m):
+        x_left = feature[i, ].T
+        x_right = feature[i, ]
+        G += x_left * x_right
+    return G
+
+def get_error(feature, label, w):
+    '''计算误差
+    input:  feature(mat):特征
+            label(mat):标签
+            w(mat):线性回归模型的参数
+    output: 损失函数值
+    '''
+    return (label - feature * w).T * (label - feature * w) / 2
+
+def get_min_m(feature, label, sigma, delta, d, w, g):
+    '''计算步长中最小的值m
+    input:  feature(mat):特征
+            label(mat):标签
+            sigma(float),delta(float):全局牛顿法的参数
+            d(mat):负的一阶导数除以二阶导数值
+            g(mat):一阶导数值
+    output: m(int):最小m值
+    '''
+    m = 0
+    while True:
+        w_new = w + pow(sigma, m) * d
+        left = get_error(feature, label , w_new)
+        right = get_error(feature, label , w) + delta * pow(sigma, m) * g.T * d
+        if left <= right:
+            break
+        else:
+            m += 1
+    return m           
+
+def newton(feature, label, iterMax, sigma, delta):
+    '''牛顿法
+    input:  feature(mat):特征
+            label(mat):标签
+            iterMax(int):最大迭代次数
+            sigma(float), delta(float):牛顿法中的参数
+    output: w(mat):回归系数
+    '''
+    n = np.shape(feature)[1]
+    w = np.mat(np.zeros((n, 1)))
+    it = 0
+    while it <= iterMax:
+        # print it
+        g = first_derivativ(feature, label, w)  # 一阶导数
+        G = second_derivative(feature)  # 二阶导数
+        d = -G.I * g
+        m = get_min_m(feature, label, sigma, delta, d, w, g)  # 得到最小的m
+        w = w + pow(sigma, m) * d
+        if it % 10 == 0:
+            print "\t---- itration: ", it, " , error: ", get_error(feature, label , w)[0, 0]
+        it += 1       
+    return w
+
+def save_model(file_name, w):
+    '''保存最终的模型
+    input:  file_name(string):要保存的文件的名称
+            w(mat):训练好的线性回归模型
+    '''
+    f_result = open(file_name, "w")
+    m, n = np.shape(w)
+    for i in xrange(m):
+        w_tmp = []
+        for j in xrange(n):
+            w_tmp.append(str(w[i, j]))
+        f_result.write("\t".join(w_tmp) + "\n")
+    f_result.close()
+    
+
+if __name__ == "__main__":
+    # 1、导入数据集
+    print "----------- 1.load data ----------"
+    feature, label = load_data("data.txt")
+    # 2.1、最小二乘求解
+    print "----------- 2.training ----------"
+    # print "\t ---------- least_square ----------"
+    # w_ls = least_square(feature, label)
+    # 2.2、牛顿法
+    print "\t ---------- newton ----------"
+    w_newton = newton(feature, label, 50, 0.1, 0.5)
+    # 3、保存最终的结果
+    print "----------- 3.save result ----------"
+    save_model("weights", w_newton)
+