梯度下降算法的python实现
简介
本文使用python实现了梯度下降算法,支持y = Wx+b的线性回归，
目前支持批量梯度算法和随机梯度下降算法(bs=1)
也支持输入特征向量的x维度小于3的图像可视化
代码要求python版本>3.4
代码
'''
梯度下降算法
Batch Gradient Descent
Stochastic Gradient Descent SGD
'''
__author__ = 'epleone'
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import sys
# 使用随机数种子， 让每次的随机数生成相同，方便调试
# np.random.seed(111111111)
class GradientDescent(object):
eps = 1.0e-8
max_iter = 1000000 # 暂时不需要
dim = 1
func_args = [2.1, 2.7] # [w_0, .., w_dim, b]
def __init__(self, func_arg=None, N=1000):
self.data_num = N
if func_arg is not None:
self.FuncArgs = func_arg
self._getData()
def _getData(self):
x = 20 * (np.random.rand(self.data_num, self.dim) - 0.5)
b_1 = np.ones((self.data_num, 1), dtype=np.float)
# x = np.concatenate((x, b_1), axis=1)
self.x = np.concatenate((x, b_1), axis=1)
def func(self, x):
# noise太大的话， 梯度下降法失去作用
noise = 0.01 * np.random.randn(self.data_num) + 0
w = np.array(self.func_args)
# y1 = w * self.x[0, ] # 直接相乘
y = np.dot(self.x, w) # 矩阵乘法
y += noise
return y
@property
def FuncArgs(self):
return self.func_args
@FuncArgs.setter
def FuncArgs(self, args):
if not isinstance(args, list):
raise Exception(
'args is not list, it should be like [w_0, ..., w_dim, b]')
if len(args) == 0:
raise Exception('args is empty list!!')
if len(args) == 1:
args.append(0.0)
self.func_args = args
self.dim = len(args) - 1
self._getData()
@property
def EPS(self):
return self.eps
@EPS.setter
def EPS(self, value):
if not isinstance(value, float) and not isinstance(value, int):
raise Exception("The type of eps should be an float number")
self.eps = value
def plotFunc(self):
# 一维画图
if self.dim == 1:
# x = np.sort(self.x, axis=0)
x = self.x
y = self.func(x)
fig, ax = plt.subplots()
ax.plot(x, y, 'o')
ax.set(xlabel='x ', ylabel='y', title='Loss Curve')
ax.grid()
plt.show()
# 二维画图
if self.dim == 2:
# x = np.sort(self.x, axis=0)
x = self.x
y = self.func(x)
xs = x[:, 0]
ys = x[:, 1]
zs = y
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(xs, ys, zs, c='r', marker='o')
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.show()
else:
# plt.axis('off')
plt.text(
0.5,
0.5,
"The dimension(x.dim > 2) \n is too high to draw",
size=17,
rotation=0.,
ha="center",
va="center",
bbox=dict(
boxstyle="round",
ec=(1., 0.5, 0.5),
fc=(1., 0.8, 0.8), ))
plt.draw()
plt.show()
# print('The dimension(x.dim > 2) is too high to draw')
# 梯度下降法只能求解凸函数
def _gradient_descent(self, bs, lr, epoch):
x = self.x
# shuffle数据集没有必要
# np.random.shuffle(x)
y = self.func(x)
w = np.ones((self.dim + 1, 1), dtype=float)
for e in range(epoch):
print('epoch:' + str(e), end=',')
# 批量梯度下降，bs为1时 等价单样本梯度下降
for i in range(0, self.data_num, bs):
y_ = np.dot(x[i:i + bs], w)
loss = y_ - y[i:i + bs].reshape(-1, 1)
d = loss * x[i:i + bs]
d = d.sum(axis=0) / bs
d = lr * d
d.shape = (-1, 1)
w = w - d
y_ = np.dot(self.x, w)
loss_ = abs((y_ - y).sum())
print('\tLoss = ' + str(loss_))
print('拟合的结果为:', end=',')
print(sum(w.tolist(), []))
print()
if loss_ < self.eps:
print('The Gradient Descent algorithm has converged!!\n')
break
pass
def __call__(self, bs=1, lr=0.1, epoch=10):
if sys.version_info < (3, 4):
raise RuntimeError('At least Python 3.4 is required')
if not isinstance(bs, int) or not isinstance(epoch, int):
raise Exception(
"The type of BatchSize/Epoch should be an integer number")
self._gradient_descent(bs, lr, epoch)
pass
pass
if __name__ == "__main__":
if sys.version_info < (3, 4):
raise RuntimeError('At least Python 3.4 is required')
gd = GradientDescent([1.2, 1.4, 2.1, 4.5, 2.1])
# gd = GradientDescent([1.2, 1.4, 2.1])
print("要拟合的参数结果是: ")
print(gd.FuncArgs)
print("===================\n\n")
# gd.EPS = 0.0
gd.plotFunc()
gd(10, 0.01)
print("Finished!")