受限玻尔兹曼机(Restricted Boltzmann Machine, RBM)是一种基于能量模型的神经网络模型,在Hinton提出针对其的训练算法(对比分歧算法)后,RBM得到了更多的关注,利用RBM的堆叠可以构造出深层的神经网络模型——深度信念网(Deep Belief Net, DBN)。下面简单介绍二值型RBM的主要内容。
RBM的网络结构如下图所示:
RBM中包括两层,即:
由上图可知,在同一层中,如上图中的可见层,在可见层中,其节点之间是没有连接的,而在层与层之间,其节点是全连接的,这是RBM最重要的结构特征:层内无连接,层间全连接
。
在RBM的模型中,有如下的性质:
当给定可见层神经元的状态时。各隐藏层神经元的之间是否激活是条件独立的;反之也同样成立。
下面给出RBM模型的数学化定义:
如图:
(图片来自参考文献1)
实验代码
# coding:UTF-8
import numpy as np
import random as rd
def load_data(file_name):
data = []
f = open(file_name)
for line in f.readlines():
lines = line.strip().split("\t")
tmp = []
for x in lines:
tmp.append(float(x) / 255.0)
data.append(tmp)
f.close()
return data
def sigmrnd(P):
m, n = np.shape(P)
X = np.mat(np.zeros((m, n)))
P_1 = sigm(P)
for i in xrange(m):
for j in xrange(n):
r = rd.random()
if P_1[i, j] >= r:
X[i, j] = 1
return X
def sigm(P):
return 1.0 / (1 + np.exp(-P))
# step_1: load data
datafile = "b.txt"
data = np.mat(load_data(datafile))
m, n = np.shape(data)
# step_2: initialize
num_epochs = 10
batch_size = 100
input_dim = n
hidden_sz = 100
alpha = 1
momentum = 0.1
W = np.mat(np.zeros((hidden_sz, input_dim)))
vW = np.mat(np.zeros((hidden_sz, input_dim)))
b = np.mat(np.zeros((input_dim, 1)))
vb = np.mat(np.zeros((input_dim, 1)))
c = np.mat(np.zeros((hidden_sz, 1)))
vc = np.mat(np.zeros((hidden_sz, 1)))
# step_3: training
print "Start to train RBM: "
num_batches = int(m / batch_size)
for i in xrange(num_epochs):
kk = np.random.permutation(range(m))
err = 0.0
for j in xrange(num_batches):
batch = data[kk[j * batch_size:(j + 1) * batch_size], ]
v1 = batch
h1 = sigmrnd(np.ones((batch_size, 1)) * c.T + v1 * W.T)
v2 = sigmrnd(np.ones((batch_size, 1)) * b.T + h1 * W)
h2 = sigm(np.ones((batch_size, 1)) * c.T + v2 * W.T)
c1 = h1.T * v1
c2 = h2.T * v2
vW = momentum * vW + alpha * (c1 - c2) / batch_size
vb = momentum * vb + alpha * sum(v1 - v2).T / batch_size
vc = momentum * vc + alpha * sum(h1 - h2).T / batch_size
W = W + vW
b = b + vb
c = c + vc
#cal_err
err_result = v1 - v2
err_1 = 0.0
m_1, n_1 = np.shape(err_result)
for x in xrange(m_1):
for y in xrange(n_1):
err_1 = err_1 + err_result[x, y] ** 2
err = err + err_1 / batch_size
#print i,j,err
print i, err / num_batches
#print W
m_2,n_2 = np.shape(W)
for i in xrange(m_2):
for j in xrange(n_2):
print str(W[i, j]) + " ",
print "\n",