受限的玻尔兹曼机

 

分类： 统计机器学习算法理论 2013-07-31 15:21  425人阅读  评论(1)  收藏  举报

将matlab代码http://code.google.com/p/matrbm/中rbmBB改写成Python代码，如下，参考文献为：

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()

程序中数据下载地址为： http://download.csdn.net/detail/zc02051126/5845977
产生的结果图片如下：

数据解释：

程序中变量data存储了数据，data的维数为784x5000，每一列代表一幅手写数字的图像数据，每一列中包括了784个像素，把这784个像素转化成28X28的矩阵数据，显示出来即可看出对应的数字，以第0列的数据为例，其手写数字为

实现的代码为：

 c = data[:,0]
 d = c.reshape(28,28,order='F')
 d = d.transpose()
 plt.imshow(d)
 plt.show()