new_contents: '''Train a Siamese MLP on pairs of digits from the MNIST dataset.
  
  It follows Hadsell-et-al.'06 [1] by computing the Euclidean distance on the
  output of the shared network and by optimizing the contrastive loss (see paper
  for mode details).
  
  [1] "Dimensionality Reduction by Learning an Invariant Mapping"
      http://yann.lecun.com/exdb/publis/pdf/hadsell-chopra-lecun-06.pdf
  
  Run on GPU: THEANO_FLAGS=mode=FAST_RUN,device=gpu,floatX=float32 python mnist_siamese_graph.py
  
  Get to 99.5% test accuracy after 20 epochs.
  3 seconds per epoch on a Titan X GPU
  '''
  from __future__ import absolute_import
  from __future__ import print_function
  import numpy as np
  np.random.seed(1337)  # for reproducibility
  
  import random
  from keras.datasets import mnist
  from keras.models import Sequential, Graph
  from keras.layers.core import *
  from keras.optimizers import SGD, RMSprop
  from keras import backend as K
  
  
  def euclidean_distance(inputs):
      assert len(inputs) == 2, \
          'Euclidean distance needs 2 inputs, %d given' % len(inputs)
      u, v = inputs.values()
      return K.sqrt((K.square(u - v)).sum(axis=1, keepdims=True))
  
  
  def contrastive_loss(y, d):
      """ Contrastive loss from Hadsell-et-al.'06
          http://yann.lecun.com/exdb/publis/pdf/hadsell-chopra-lecun-06.pdf
      """
      margin = 1
      return K.mean(y * K.square(d) + (1 - y) * K.square(K.maximum(margin - d, 0)))
  
  
  def create_pairs(x, digit_indices):
      """ Positive and negative pair creation.
          Alternates between positive and negative pairs.
      """
      pairs = []
      labels = []
      n = min([len(digit_indices[d]) for d in range(10)]) - 1
      for d in range(10):
          for i in range(n):
              z1, z2 = digit_indices[d][i], digit_indices[d][i+1]
              pairs += [[x[z1], x[z2]]]
              inc = random.randrange(1, 10)
              dn = (d + inc) % 10
              z1, z2 = digit_indices[d][i], digit_indices[dn][i]
              pairs += [[x[z1], x[z2]]]
              labels += [1, 0]
      return np.array(pairs), np.array(labels)
  
  
  def create_base_network(in_dim):
      """ Base network to be shared (eq. to feature extraction).
      """
      seq = Sequential()
      seq.add(Dense(128, input_shape=(in_dim,), activation='relu'))
      seq.add(Dropout(0.1))
      seq.add(Dense(128, activation='relu'))
      seq.add(Dropout(0.1))
      seq.add(Dense(128, activation='relu'))
      return seq
  
  
  def compute_accuracy(predictions, labels):
      """ Compute classification accuracy with a fixed threshold on distances.
      """
      return labels[predictions.ravel() < 0.5].mean()
  
  
  # the data, shuffled and split between tran and test sets
  (X_train, y_train), (X_test, y_test) = mnist.load_data()
  X_train = X_train.reshape(60000, 784)
  X_test = X_test.reshape(10000, 784)
  X_train = X_train.astype('float32')
  X_test = X_test.astype('float32')
  X_train /= 255
  X_test /= 255
  in_dim = 784
  nb_epoch = 20
  
  # create training+test positive and negative pairs
  digit_indices = [np.where(y_train == i)[0] for i in range(10)]
  tr_pairs, tr_y = create_pairs(X_train, digit_indices)
  
  digit_indices = [np.where(y_test == i)[0] for i in range(10)]
  te_pairs, te_y = create_pairs(X_test, digit_indices)
  
  # network definition
  base_network = create_base_network(in_dim)
  
  g = Graph()
  g.add_input(name='input_a', input_shape=(in_dim,))
  g.add_input(name='input_b', input_shape=(in_dim,))
  g.add_shared_node(base_network, name='shared', inputs=['input_a', 'input_b'],
                    merge_mode='join')
  g.add_node(Lambda(euclidean_distance), name='d', input='shared')
  g.add_output(name='output', input='d')
  
  # train
  rms = RMSprop()
  g.compile(loss={'output': contrastive_loss}, optimizer=rms)
  g.fit({'input_a': tr_pairs[:, 0], 'input_b': tr_pairs[:, 1], 'output': tr_y},
        validation_data={'input_a': te_pairs[:, 0], 'input_b': te_pairs[:, 1], 'output': te_y},
        batch_size=128, nb_epoch=nb_epoch)
  
  # compute final accuracy on training and test sets
  pred = g.predict({'input_a': tr_pairs[:, 0], 'input_b': tr_pairs[:, 1]})['output']
  tr_acc = compute_accuracy(pred, tr_y)
  pred = g.predict({'input_a': te_pairs[:, 0], 'input_b': te_pairs[:, 1]})['output']
  te_acc = compute_accuracy(pred, te_y)
  
  print('* Accuracy on training set: %0.2f%%' % (100 * tr_acc))
  print('* Accuracy on test set: %0.2f%%' % (100 * te_acc))
  
subject: add siamese example use graph model take pairs of digits as input