FairWalk

Python3 implementation of the fairwalk algorithm Tahleen Rahman, Bartlomiej Surma, Michael Backes and Yang Zhang. Rahman, Tahleen, et al. "Fairwalk: towards fair graph embedding." Proceedings of the 2019 International Joint Conferences on Artifical Intelligence (IJCAI). IJCAI. 2019.‏

Installation

python setup.py install

Usage

import networkx as nx
from fairwalk import FairWalk

# Create a graph
graph = nx.fast_gnp_random_graph(n=100, p=0.5)
n = len(graph.nodes())
node2group = {node: group for node, group in zip(graph.nodes(), (5*np.random.random(n)).astype(int))}
nx.set_node_attributes(graph, node2group, 'group')

# Precompute probabilities and generate walks - **ON WINDOWS ONLY WORKS WITH workers=1**
model = FairWalk(graph, dimensions=64, walk_length=30, num_walks=200, workers=4)  # Use temp_folder for big graphs

# Embed nodes
model = model.fit(window=10, min_count=1, batch_words=4)  # Any keywords acceptable by gensim.Word2Vec can be passed, `diemnsions` and `workers` are automatically passed (from the FairWalk constructor)

# Look for most similar nodes
model.wv.most_similar('2')  # Output node names are always strings

# Save embeddings for later use
model.wv.save_word2vec_format(EMBEDDING_FILENAME)

# Save model for later use
model.save(EMBEDDING_MODEL_FILENAME)

# Embed edges using Hadamard method
from fairwalk.edges import HadamardEmbedder

edges_embs = HadamardEmbedder(keyed_vectors=model.wv)

# Look for embeddings on the fly - here we pass normal tuples
edges_embs[('1', '2')]
''' OUTPUT
array([ 5.75068220e-03, -1.10937878e-02,  3.76693785e-01,  2.69105062e-02,
       ... ... ....
       ..................................................................],
      dtype=float32)
'''

# Get all edges in a separate KeyedVectors instance - use with caution could be huge for big networks
edges_kv = edges_embs.as_keyed_vectors()

# Look for most similar edges - this time tuples must be sorted and as str
edges_kv.most_similar(str(('1', '2')))

# Save embeddings for later use
edges_kv.save_word2vec_format(EDGES_EMBEDDING_FILENAME)

Parameters

fairwalk.FairWalk

• FairWalk constructor:

  1. graph: The first positional argument has to be a networkx graph. Node names must be all integers or all strings. On the output model they will always be strings.
  2. dimensions: Embedding dimensions (default: 128)
  3. walk_length: Number of nodes in each walk (default: 80)
  4. num_walks: Number of walks per node (default: 10)
  5. p: Return hyper parameter (default: 1)
  6. q: Inout parameter (default: 1)
  7. weight_key: On weighted graphs, this is the key for the weight attribute (default: 'weight')
  8. workers: Number of workers for parallel execution (default: 1)
  9. sampling_strategy: Node specific sampling strategies, supports setting node specific 'q', 'p', 'num_walks' and 'walk_length'. Use these keys exactly. If not set, will use the global ones which were passed on the object initialization`
  10. quiet: Boolean controlling the verbosity. (default: False)
  11. temp_folder: String path pointing to folder to save a shared memory copy of the graph - Supply when working on graphs that are too big to fit in memory during algorithm execution.

• FairWalk.fit method: Accepts any key word argument acceptable by gensim.Word2Vec

fairwalk.EdgeEmbedder

EdgeEmbedder is an abstract class which all the concrete edge embeddings class inherit from. The classes are AverageEmbedder, HadamardEmbedder, WeightedL1Embedder and WeightedL2Embedder which their practical definition could be found in the paper on table 1 Notice that edge embeddings are defined for any pair of nodes, connected or not and even node with itself.

• Constructor:

  1. keyed_vectors: A gensim.models.KeyedVectors instance containing the node embeddings
  2. quiet: Boolean controlling the verbosity. (default: False)

• EdgeEmbedder.__getitem__(item) method, better known as EdgeEmbedder[item]:

  1. item - A tuple consisting of 2 nodes from the keyed_vectors passed in the constructor. Will return the embedding of the edge.

• EdgeEmbedder.as_keyed_vectors method: Returns a gensim.models.KeyedVectors instance with all possible node pairs in a sorted manner as string. For example, for nodes ['1', '2', '3'] we will have as keys "('1', '1')", "('1', '2')", "('1', '3')", "('2', '2')", "('2', '3')" and "('3', '3')".

Caveats

• Node names in the input graph must be all strings, or all ints
• Parallel execution not working on Windows (joblib known issue). To run non-parallel on Windows pass workers=1 on the FairWalk's constructor