算法python实现

1.算法python代码

包含Normal Equations，批量梯度下降和随机梯度下降，这里的代码跟Logistic回归的代码类似

# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt
import numpy as np

class LinearRegression(object):

    def __init__(self):
        self._history_w = []
        self._cost = []

    def load_input_data(self, data_file):
        with open(data_file) as f:
            input_x = []
            input_y = []
            for line in f:
                [x0, x1, y] = line.split()
                input_x.append([float(x0), float(x1)])
                input_y.append(float(y))
        self._input_x = np.array(input_x)
        self._input_y = np.array(input_y).T

    def normal_equations(self):  # 用矩阵的计算直接得到w
        xtx = np.dot(self._input_x.T, self._input_x)
        xtx_inverse = np.linalg.inv(xtx)
        tmp = np.dot(xtx_inverse, self._input_x.T)
        self._final_w = np.inner(tmp, self._input_y) # (X^T * X)^-1 * X^T * Y
        return self._final_w

    def cost_function(self, w):  # 成本函数
        tmp = np.inner(self._input_x, w)
        tmp = tmp - self._input_y
        return np.inner(tmp.T, tmp)

    def batch_gradient_descent(self, iter_num, iter_rate): #批量梯度下降
        (data_num, features) = np.shape(self._input_x)
        w = np.ones(features)
        for i in range(iter_num):
            inner = np.inner(self._input_x, w)
            delta = inner - self._input_y
            w = w - iter_rate * np.inner(self._input_x.T, delta) #w的迭代
            self._history_w.append(w)
            self._cost.append(self.cost_function(w))
        self._final_w = w
        return w

    def stochastic_gradient_descent(self, iter_num, iter_rate): # 随机梯度下降
        (data_num, features) = np.shape(self._input_x)
        w = np.ones(features)
        data_range = range(data_num)
        for i in range(iter_num):
            for j in data_range:
                iter_rate = 4/(1.0+j+i) + 0.01
                inner = np.inner(self._input_x[j], w)
                delta = inner - self._input_y[j]
                w = w - iter_rate * delta* self._input_x[j] #w的迭代
                self._history_w.append(w)
                self._cost.append(self.cost_function(w))
        self._final_w = w
        return w

2. python数据显示

在同一个类中添加如下代码

    def draw_result(self, title):
        plt.figure(1)
        x1 = [x[1] for x in self._input_x]
        plt.scatter(x1, self._input_y, color='b', s=20, marker=".")
        plt.xlabel('x')
        plt.ylabel('x')
        def f(x):
            return (self._final_w[0] + self._final_w[1]*x)
        x2 = np.array([self._input_x.min(axis=0)[1], self._input_x.max(axis=0)[1]])
        plt.plot(x2, f(x2), 'b-', lw=1)
        plt.title(title)
        plt.show()

    def draw_cost_function(self, title):
        plt.figure(1)
        x = np.arange(len(self._cost))
        plt.scatter(x, self._cost, label='Cost', color='g', s=10, marker=".")
        plt.xlabel('x')
        plt.ylabel('Cost function')
        plt.title(title + ' Cost trend')
        plt.ylim(-0.5, 100) #限定y轴显示的区间
        plt.legend()
        plt.show()

3.数据集测试

数据集来自《机器学习实战》

https://github.com/apachecn/MachineLearning/blob/python-2.7/input/8.Regression/data.txt

3.1 Normal Equations

linear = LinearRegression()
linear.load_input_data("test.txt")
linear.normal_equations()
title = "Normal Equations"
linear.draw_result(title)

3.2 批量梯度下降

linear = LinearRegression()
linear.load_input_data("test.txt")
linear.batch_gradient_descent(iter_num=100, iter_rate=0.001)
title = "Batch Gradient Descent"
linear.draw_result(title)
linear.draw_cost_function(title)

3.2 随机梯度下降

linear = LinearRegression()
linear.load_input_data("test.txt")
linear.stochastic_gradient_descent(iter_num=5, iter_rate=0.001)
title = "Stochastic Gradient Descent"
linear.draw_result(title)
linear.draw_cost_function(title)