机器学习-线性回归 Linear Regression

# 线性回归模型算法

import numpy as np
import matplotlib.pyplot as plt


def gradient_descent(X, Y, iteration=200, learning_rate=0.067):  # 线性回归梯度下降程序

    print("running gradient descent...")

    mExamples = X.shape[0]
    nFeatures = X.shape[1]

    # 训练数据中添加一列为全0，作为x0，theta0的参数,
    # 训练集的维度为m*（n+1）
    trainX = np.zeros((mExamples, nFeatures+1))
    trainX[:, 0] = np.ones(mExamples)
    trainX[:, 1:] = X

    # 定义标签数组
    trainY = np.zeros((mExamples, 1))
    trainY[:,0] = Y

    # 初始化模型参数，维度为（n+1）*1
    parameters = np.zeros((nFeatures+1, 1))

    # 迭代模型参数
    iteration_i = 0
    while iteration_i < iteration:
        #定义梯度函数
        Z = np.dot(trainX, parameters)
        PartDeri = np.dot(trainX.T, (Z-Y))/mExamples
        #更新梯度
        parameters = parameters - learning_rate*PartDeri
        # 定义代价函数
        cost = np.sum(np.square(np.dot(trainX, parameters) - trainY) / (2.0 * mExamples))
        print("[", iteration_i, "]", "[cost]", cost)
        iteration_i = iteration_i + 1

    predict = np.dot(trainX, parameters)

    return predict


if __name__ == '__main__':

    # 创建数据集合
    X = np.arange(0, 10, 1).reshape(10, 1)
    print("X:", X)

    Y = np.ones(10)
    print("Y: ", Y)

    plt.figure()
    plt.xlim((1, 10))
    plt.ylim((-2, 2))
    # 红线为理想曲线
    plt.plot(X, Y, color='r')

    # 蓝线为拟合曲线
    predict = gradient_descent(X, Y)
    plt.plot(X, predict, color='b')
    plt.show()