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| # -*- coding: utf-8 -*-
# @Time : 19-4-16 下午3:38
# @Author : zj
"""
梯度下降法计算线性回归问题
"""
import matplotlib.pyplot as plt
import numpy as np
def load_ex1_multi_data():
"""
加载多变量数据
"""
path = '../data/coursera2.txt'
datas = []
with open(path, 'r') as f:
lines = f.readlines()
for line in lines:
datas.append(line.strip().split(','))
data_arr = np.array(datas)
data_arr = data_arr.astype(np.float)
X = data_arr[:, :2]
Y = data_arr[:, 2]
return X, Y
def load_machine_data():
"""
加载计算机硬件数据
"""
data = np.loadtxt('../data/machine.data', delimiter=',', dtype=np.str)
# print(data)
x = data[:, 2:8].astype(np.float)
y = data[:, 8].astype(np.float)
# print(x)
# print(y)
return x, y
def draw_loss(loss_list):
"""
绘制损失函数值
"""
fig = plt.figure()
plt.plot(loss_list)
plt.show()
def init_weight(size):
"""
初始化权重，使用均值为0,方差为1的标准正态分布
"""
return np.random.normal(loc=0.0, scale=1.0, size=size)
def compute_loss(w, x, y):
"""
计算损失值
"""
n = y.shape[0]
return (x.dot(w) - y).T.dot(x.dot(w) - y) / n
def using_batch_gradient_descent():
"""
批量梯度下降
"""
x, y = load_machine_data()
extend_x = np.insert(x, 0, values=np.ones(x.shape[0]), axis=1)
w = init_weight(extend_x.shape[1])
# print(w)
n = y.shape[0]
epoches = 50
alpha = 1e-9
loss_list = []
for i in range(epoches):
temp = w - alpha * extend_x.T.dot(extend_x.dot(w) - y) / n
w = temp
loss_list.append(compute_loss(w, extend_x, y))
draw_loss(loss_list)
def using_stochastic_gradient_descent():
"""
随机梯度下降
"""
x, y = load_machine_data()
extend_x = np.insert(x, 0, values=np.ones(x.shape[0]), axis=1)
w = init_weight(extend_x.shape[1])
# print(w)
print(w.shape)
# 打乱数据
np.random.shuffle(extend_x)
print(extend_x.shape)
print(y.shape)
n = y.shape[0]
epoches = 20
alpha = 1e-9
loss_list = []
for i in range(epoches):
for j in range(n):
temp = w - alpha * (extend_x[j].dot(w) - y[j]) * extend_x[j].T / 2
w = temp
loss_list.append(compute_loss(w, extend_x, y))
draw_loss(loss_list)
def using_small_batch_gradient_descent():
"""
小批量梯度下降
"""
x, y = load_machine_data()
extend_x = np.insert(x, 0, values=np.ones(x.shape[0]), axis=1)
w = init_weight(extend_x.shape[1])
# print(w)
print(w.shape)
# 打乱数据
np.random.shuffle(extend_x)
print(extend_x.shape)
print(y.shape)
# 批量大小
batch_size = 16
n = y.shape[0]
epoches = 20
alpha = 5e-9
loss_list = []
for i in range(epoches):
for j in list(range(0, n, batch_size)):
temp = w - alpha * extend_x[j:j + batch_size].T.dot(
extend_x[j:j + batch_size].dot(w) - y[j:j + batch_size]) / batch_size
w = temp
loss_list.append(compute_loss(w, extend_x, y))
draw_loss(loss_list)
if __name__ == '__main__':
# using_batch_gradient_descent()
using_stochastic_gradient_descent()
# using_small_batch_gradient_descent()
|
