受限玻尔兹曼机RBM

相关算法

python代码参考http://blog.csdn.net/zc02051126/article/details/9668439#（作少量修改与注释）

 #coding:utf8
 import matplotlib.pylab as plt
 import numpy as np
 import cPickle

 class RBM:
     def __init__(self,n_visul, n_hidden, max_epoch = 50, batch_size = 110, penalty = 2e-4):
         self.n_visible = n_visul
         self.n_hidden = n_hidden
         self.max_epoch = max_epoch
         self.batch_size = batch_size
         self.penalty = penalty
         self.w = np.random.random((self.n_visible, self.n_hidden)) * 0.1
         self.v_bias = np.zeros((1, self.n_visible))
         self.h_bias = np.zeros((1, self.n_hidden))

     def sigmoid(self, z):
         return 1.0 / (1.0 + np.exp( -z ))

     def forward(self, vis):
         return self.sigmoid(np.dot(vis.T, self.w) + self.h_bias)

     def backward(self, vis):
         return self.sigmoid(np.dot(vis, self.w.T) + self.v_bias)

     def batch(self):
         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[:N]
         np.random.shuffle(groups)
         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  #动量项
         W = self.w
         b = self.h_bias
         c = self.v_bias
         Winc  = np.zeros((self.n_visible, self.n_hidden))
         binc = np.zeros(self.n_hidden)
         cinc = np.zeros(self.n_visible)
         batch_data = self.batch()
         num_batch = len(batch_data)
         errors = []
         for epoch in range(0, self.max_epoch):
             err_sum = 0.0
             for batch in range(0, num_batch):
                 num_dims, num_cases = batch_data[batch].shape
                 data = batch_data[batch]
                 # 已知可见层，采样出隐藏层
                 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
                 # 已知隐藏层，采样出可见层
                 neg_data = self.backward(ph_states)
                 neg_data_states = np.zeros((num_cases, num_dims))
                 neg_data_states[neg_data > np.random.random((num_cases, num_dims))] = 1
                 neg_data_states = neg_data_states.transpose()
                 nh = self.forward(neg_data_states)
                 # CD算法
                 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)
                 # 刷新参数
                 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
                 err = np.linalg.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)

     def visualize(self, X):  #可视化
         D, N = X.shape
         s = int(np.sqrt(D))
         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+x:x*s+s+x , y*s+y:y*s+s+y] = z
             x = x + 1
             if(x >= num):
                 x = 0
                 y = y + 1
         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__':
     f = open('mnist.pkl', 'rb')
     training_data, validation_data, test_data = cPickle.load(f)
     training_inputs = [np.reshape(x, 784) for x in training_data[0]]
     data =training_inputs[:5000]
     data = np.array(data)
     data = data.transpose()
     rbm = Rbm(784, 100,max_epoch = 50)
     rbm.rbmBB(data)

     a = rbm.visualize(data)  #(2060L, 2060L)
     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)  #(2060L, 2060L)
     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)  #(782L, 782L)
     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)  #(291L, 291L)
     fig = plt.figure(4)
     ax = fig.add_subplot(111)
     ax.imshow(d)
     plt.title('weight value(w)')
     plt.show()