Add. Realizes the Gradient Descent

机器学习算法理论及应用/第二章——手写线性回归算法/LinearRegression/linear_regression.py

@@ -13,8 +13,6 @@ class LinearRegression:
         polynomial_degree: 是否做额外变换
         sinusoid_degree: 是否做额外变换
         normalize_data: 是否标准化数据
-
-        :return
         """
         (data_processed,
          features_mean,
@@ -28,3 +26,56 @@ class LinearRegression:
         self.polynomial_degree = polynomial_degree
         self.sinusoid_degree = sinusoid_degree
         self.normalize_data = normalize_data
+
+        num_features = self.data.shape[1]
+        self.theta = np.zeros((num_features, 1))
+
+    def train(self, alpha, num_iterations=500):
+        """
+        训练模块，执行梯度下降
+
+        alpha: 学习率
+        num_iterations: 迭代次数
+        """
+        cost_history = self.gradient_descent(alpha, num_iterations)
+        return self.theta, cost_history
+
+    def gradient_descent(self, alpha, num_iterations):
+        """
+        实际迭代模块
+
+        alpha: 学习率
+        num_iterations: 迭代次数
+        """
+        cost_history = []
+        for _ in range(num_iterations):  # 开始迭代
+            self.gradient_step(alpha)
+            cost_history.append(self.cost_function(self.data, self.labels))
+        return cost_history
+
+    def gradient_step(self, alpha):
+        """
+        梯度下降参数更新计算方法，注意是矩阵运算
+
+        alpha: 学习率
+        """
+        num_examples = self.data.shape[0]  # 当前样本个数
+        # 根据当前数据和θ获取预测值
+        prediction = LinearRegression.hypothesis(self.data, self.theta)
+        delta = prediction - self.labels  # 残差，即预测值减去真实值
+        theta = self.theta
+        # 依照小批量梯度下降法，写代码表示
+        theta = theta - alpha * (1/num_examples)*(np.dot(delta.T, self.data)).T
+        self.theta = theta  # 计算完theta后更新当前theta
+
+    @staticmethod
+    def hypothesis(data, theta):
+        """
+        获取预测值
+
+        :param data:  矩阵数据
+        :param theta:  权重θ
+        :return: 返回预测值
+        """
+        predictions = np.dot(data, theta)
+        return predictions