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I am setting up a Recurrent Neural Network, where I have a time series of features vectors (N x D), where each of the N columns corresponds to an "event". I am given the evolution of the coordinates of the event in another N x 3 matrix. Instead of just feeding the network with an (N x D + 3) matrix, I want to build a graph of events in order to make use of Graph Convolutions as well. Thus, if I have a time series of length t, I am dealing with an input of dimensionality t x N x D as well as t x N x 3, as both the features as well as the coordinates of the single "events" evolve.

For the case of single event classification I already built a method to construct the dense adjacency matrix of the coordinates of the N events. This involves calculating the pairwise distances of each of the N coordinates and applying a Gaussian Kernel.

To be more precise, I obtain the distance matrix according to this question's answer. I can however not figure out how to generalize this approach to a setting, where I have t differnt N x D coordinate systems without iterating over those (which would be too costly).

This is the tensorflow code I am currently using to obtain the distance matrix given the coordinates.

coordinate_norms = tf.reduce_sum(coordinates * coordinates, 1)
coordinate_norms = tf.reshape(coordinate_norms, [-1, 1])
distances = coordinate_norms - 2 * tf.matmul(coordinates, tf.transpose(coordinates)) + tf.transpose(coordinate_norms)

If I simply use the approch here, the tensors dimension are incorrect.

Jeremy Bastard
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1 Answers1

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I found out, that it can be done easily just wrapping the computation of the distance matrix into a function and then using tf.map_fn in order to map it along the desired axis of the input tensor.

def calculate_distance(coordiantes):
   coordinate_norms = tf.reduce_sum(coordinates * coordinates, 1)
   coordinate_norms = tf.reshape(coordinate_norms, [-1, 1])
   distances = coordinate_norms - 2 * tf.matmul(coordinates, tf.transpose(coordinates)) + tf.transpose(coordinate_norms)

d = tf.map_fn(calculate_distance, X)
Jeremy Bastard
  • 13
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