受限的玻尔兹曼机
1 A Tutorial on Stochastic Approximation Algorithms for Training Restricted Boltzmann Machines and Deep Belief Nets
2 Inductive Principles for Learning Restricted Boltzmann Machines
3 Training products of experts by minimizing contrastive divergence
4 受限波尔兹曼机简介
import matplotlib.pylab as plt
import numpy as np
import random
from scipy.linalg import norm
import PIL.Image
class Rbm:
def __init__(self,n_visul, n_hidden, max_epoch = 50, batch_size = 110, penalty = 2e-4, anneal = False, w = None, v_bias = None, h_bias = None):
self.n_visible = n_visul
self.n_hidden = n_hidden
self.max_epoch = max_epoch
self.batch_size = batch_size
self.penalty = penalty
self.anneal = anneal
if w is None:
self.w = np.random.random((self.n_visible, self.n_hidden)) * 0.1
if v_bias is None:
self.v_bias = np.zeros((1, self.n_visible))
if h_bias is None:
self.h_bias = np.zeros((1, self.n_hidden))
def sigmod(self, z):
return 1.0 / (1.0 + np.exp( -z ))
def forward(self, vis):
#if(len(vis.shape) == 1):
#vis = np.array([vis])
#vis = vis.transpose()
#if(vis.shape[1] != self.w.shape[0]):
vis = vis.transpose()
pre_sigmod_input = np.dot(vis, self.w) + self.h_bias
return self.sigmod(pre_sigmod_input)
def backward(self, vis):
#if(len(vis.shape) == 1):
#vis = np.array([vis])
#vis = vis.transpose()
#if(vis.shape[0] != self.w.shape[1]):
back_sigmod_input = np.dot(vis, self.w.transpose()) + self.v_bias
return self.sigmod(back_sigmod_input)
def batch(self):
eta = 0.1
momentum = 0.5
d, N = self.x.shape
num_batchs = int(round(N / self.batch_size)) + 1
groups = np.ravel(np.repeat([range(0, num_batchs)], self.batch_size, axis = 0))
groups = groups[0 : N]
perm = range(0, N)
random.shuffle(perm)
groups = groups[perm]
batch_data = []
for i in range(0, num_batchs):
index = groups == i
batch_data.append(self.x[:, index])
return batch_data
def rbmBB(self, x):
self.x = x
eta = 0.1
momentum = 0.5
W = self.w
b = self.h_bias
c = self.v_bias
Wavg = W
bavg = b
cavg = c
Winc = np.zeros((self.n_visible, self.n_hidden))
binc = np.zeros(self.n_hidden)
cinc = np.zeros(self.n_visible)
avgstart = self.max_epoch - 5;
batch_data = self.batch()
num_batch = len(batch_data)
oldpenalty= self.penalty
t = 1
errors = []
for epoch in range(0, self.max_epoch):
err_sum = 0.0
if(self.anneal):
penalty = oldpenalty - 0.9 * epoch / self.max_epoch * oldpenalty
for batch in range(0, num_batch):
num_dims, num_cases = batch_data[batch].shape
data = batch_data[batch]
#forward
ph = self.forward(data)
ph_states = np.zeros((num_cases, self.n_hidden))
ph_states[ph > np.random.random((num_cases, self.n_hidden))] = 1
#backward
nh_states = ph_states
neg_data = self.backward(nh_states)
neg_data_states = np.zeros((num_cases, num_dims))
neg_data_states[neg_data > np.random.random((num_cases, num_dims))] = 1
#forward one more time
neg_data_states = neg_data_states.transpose()
nh = self.forward(neg_data_states)
nh_states = np.zeros((num_cases, self.n_hidden))
nh_states[nh > np.random.random((num_cases, self.n_hidden))] = 1
#update weight and biases
dW = np.dot(data, ph) - np.dot(neg_data_states, nh)
dc = np.sum(data, axis = 1) - np.sum(neg_data_states, axis = 1)
db = np.sum(ph, axis = 0) - np.sum(nh, axis = 0)
Winc = momentum * Winc + eta * (dW / num_cases - self.penalty * W)
binc = momentum * binc + eta * (db / num_cases);
cinc = momentum * cinc + eta * (dc / num_cases);
W = W + Winc
b = b + binc
c = c + cinc
self.w = W
self.h_bais = b
self.v_bias = c
if(epoch > avgstart):
Wavg -= (1.0 / t) * (Wavg - W)
cavg -= (1.0 / t) * (cavg - c)
bavg -= (1.0 / t) * (bavg - b)
t += 1
else:
Wavg = W
bavg = b
cavg = c
#accumulate reconstruction error
err = norm(data - neg_data.transpose())
err_sum += err
print epoch, err_sum
errors.append(err_sum)
self.errors = errors
self.hiden_value = self.forward(self.x)
h_row, h_col = self.hiden_value.shape
hiden_states = np.zeros((h_row, h_col))
hiden_states[self.hiden_value > np.random.random((h_row, h_col))] = 1
self.rebuild_value = self.backward(hiden_states)
self.w = Wavg
self.h_bais = b
self.v_bias = c
def visualize(self, X):
D, N = X.shape
s = int(np.sqrt(D))
if s == int(np.floor(s)):
num = int(np.ceil(np.sqrt(N)))
a = np.zeros((num*s + num + 1, num * s + num + 1)) - 1.0
x = 0
y = 0
for i in range(0, N):
z = X[:,i]
z = z.reshape(s,s,order='F')
z = z.transpose()
a[x*s+1+x - 1:x*s+s+x , y*s+1+y - 1:y*s+s+y ] = z
x = x + 1
if(x >= num):
x = 0
y = y + 1
d = True
else:
a = X
return a
def readData(path):
data = []
for line in open(path, 'r'):
ele = line.split(' ')
tmp = []
for e in ele:
if e != '':
tmp.append(float(e.strip(' ')))
data.append(tmp)
return data
if __name__ == '__main__':
data = readData('data.txt')
data = np.array(data)
data = data.transpose()
rbm = Rbm(784, 100,max_epoch = 50)
rbm.rbmBB(data)
a = rbm.visualize(data)
fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.imshow(a)
plt.title('original data')
rebuild_value = rbm.rebuild_value.transpose()
b = rbm.visualize(rebuild_value)
fig = plt.figure(2)
ax = fig.add_subplot(111)
ax.imshow(b)
plt.title('rebuild data')
hidden_value = rbm.hiden_value.transpose()
c = rbm.visualize(hidden_value)
fig = plt.figure(3)
ax = fig.add_subplot(111)
ax.imshow(c)
plt.title('hidden data')
w_value = rbm.w
d = rbm.visualize(w_value)
fig = plt.figure(4)
ax = fig.add_subplot(111)
ax.imshow(d)
plt.title('weight value(w)')
plt.show()
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