python梯度下降算法的实现

本文实例为大家分享了python实现梯度下降算法的具体代码,供大家参考,具体内容如下

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!")

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