# -*- coding: utf-8 -*-
"""
Created on Wed Aug 30 15:27:51 2017
@author: liuxy
"""
import numpy as np
import matplotlib.pyplot as plt
def gen_data(size):
x1 = np.arange(0, size, 1)
x2 = np.arange(0, size, 1)
e = np.random.normal(0, 3, size)
y = 2*x1 + x2 + e
return np.array([x1, x2, y])
def compute_gradient_full(data, w):
X1 = data[0]
X2 = data[1]
Y = data[2]
N = len(Y)
g1 = np.sum(2*X1*2*(X1*w[0] - Y))/N
g2 = np.sum(2*X2*(X2*w[1] - Y))/N
return np.array([g1, g2])
def compute_gradient_sgd(data, w):
X1 = data[0]
X2 = data[1]
Y = data[2]
idx = np.random.randint(0, len(Y)-1);
x1 = X1[idx]
x2 = X2[idx]
y = Y[idx]
g1 = 2
g1 = 2*x1*2*(x1*w[0] - y)
g2 = 2*x2*(x2*w[1] - y)
return np.array([g1, g2])
def Optimizer(data, learning_rate, num_iterator, Wts, method):
w = Wts[0]
for i in range(num_iterator):
if ('full' == method):
g = compute_gradient_full(data, w)
if ('sgd' == method):
g = compute_gradient_sgd(data, w)
w = w - learning_rate * g
Wts.append(w)
data = gen_data(100)
lr = 0.00005
w = [80,59]
num = 100
Weights_full = []
Weights_full.append(w)
Optimizer(data, lr, num, Weights_full, 'sgd')
w1 = np.arange(0, 100, 0.2)
w2 = np.arange(0, 100, 0.2)
W1, W2 = np.meshgrid(w1, w2)
X1 = data[0]
X2 = data[1]
Y = data[2]
Z = []
for i in range(len(w1)):
ls = []
for j in range(len(w2)):
L = (np.sum((X1*w1[i] + X2*w2[j] - Y)**2))/len(Y)
ls.append(L)
Z.append(ls)
Zs = np.array(Z)
plt.contour(W1, W2, Zs)
WWW = np.array(Weights_full)
plt.scatter(WWW[:,0], WWW[:,1])
plt.plot(WWW[:,0], WWW[:,1])
上图分别为 full batch 与 sgd 的效果图
