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Word Embeddings
print("random walks generated already, skipping")
return
f = open(ofile, "w")
for i in range(E.shape[0]): # for each vertex
if i % 100 == 0:
print("{:d} random walks generated from {:d} vertices"
.format(n * i, i))
for j in range(n): # construct n random walks
curr = i
walk = [curr]
target_nodes = np.nonzero(E[curr])[1]
for k in range(l): # each of max length l
# should we restart?
if np.random.random() < alpha and len(walk) > 5:
break
# choose one outgoing edge and append to walk
try:
curr = np.random.choice(target_nodes)
walk.append(curr)
target_nodes = np.nonzero(E[curr])[1]
except ValueError:
continue
f.write("{:s}\n".format(" ".join([str(x) for x in walk])))
print("{:d} random walks generated from {:d} vertices, COMPLETE"
.format(n * i, i))
f.close()
# construct random walks (caution: very long process!)
construct_random_walks(E, NUM_WALKS_PER_VERTEX, RESTART_PROB, MAX_
PATH_LENGTH, RANDOM_WALKS_FILE)
A few lines from the RANDOM_WALKS_FILE are shown below. You could imagine
that these look like sentences in a language where the vocabulary of words is all
the node IDs in our graph. We have learned that word embeddings exploit the
structure of language to generate a distributional representation for words. Graph
embedding schemes such as DeepWalk and node2vec do the exact same thing with
these "sentences" created out of random walks. Such embeddings are able to capture
similarities between nodes in a graph that go beyond immediate neighbors, as we
shall see as follows:
0 1405 4845 754 4391 3524 4282 2357 3922 1667
0 1341 456 495 1647 4200 5379 473 2311
[ 256 ]