Doing pairwise distance computation with TensorFlow

Question

I'm trying to impelement this article: http://ronan.collobert.com/pub/matos/2008_deep_icml.pdf Specfically the equation (3) from section 2.

Shortly I want to do a pairwise distance computation for the features of each mini-batch and insert this loss to the general network loss. I have only the Tesnor of the batch (16 samples), the labels tensor of the batch and the batch feature Tensor.

After looking for quite a while I still couldn't figure out the following:

1) How do I divide the batch for Positive (i.e. same label) and negative pairs. Since Tensor are not iterateble I can't figure out how to get which sample have which label and then divide my vector, or get which indices of the tensor belong to each class.

2) How can I do pairwise distance calculation for some of the indices in the batch tensor?

3) I also need to define a new distance function for negative examples

Overall, I need to get which indices belong to which class, do a positive pair-wise distace calculation for all positive pairs. And do another calculation for all negative pairs. Then sum it all up and add it to the network loss.

Any help (to one of more of the 3 issues) would be highly appreciated.

Answer 1

1) You should do the pair sampling before feeding the data into a session. Label every pair a boolean label, say y = 1 for matched-pair, 0 otherwise.

2) 3) Just calculate both pos/neg terms for every pair, and let the 0-1 label y to choose which to add to the loss.

---

First create placeholders, y_ is for boolean labels.

dim = 64
x1_ = tf.placeholder('float32', shape=(None, dim))
x2_ = tf.placeholder('float32', shape=(None, dim))
y_ = tf.placeholder('uint8', shape=[None])   # uint8 for boolean

Then the loss tensor can be created by the function.

def loss(x1, x2, y):
    # Euclidean distance between x1,x2
    l2diff = tf.sqrt( tf.reduce_sum(tf.square(tf.sub(x1, x2)),
                                    reduction_indices=1))

    # you can try margin parameters
    margin = tf.constant(1.)     

    labels = tf.to_float(y)

    match_loss = tf.square(l2diff, 'match_term')
    mismatch_loss = tf.maximum(0., tf.sub(margin, tf.square(l2diff)), 'mismatch_term')

    # if label is 1, only match_loss will count, otherwise mismatch_loss
    loss = tf.add(tf.mul(labels, match_loss), \
                  tf.mul((1 - labels), mismatch_loss), 'loss_add')

    loss_mean = tf.reduce_mean(loss)
    return loss_mean

loss_ = loss(x1_, x2_, y_)

Then feed your data (random generated for example):

batchsize = 4
x1 = np.random.rand(batchsize, dim)
x2 = np.random.rand(batchsize, dim)
y = np.array([0,1,1,0])

l = sess.run(loss_, feed_dict={x1_:x1, x2_:x2, y_:y})