This repository contains an unofficial implementation of

Graph signal processing for directed graphs based on the Hermitian Laplacian.

Furutani, S., Shibahara, T., Akiyama, M., Hato, K., & Aida, M.

Joint European Conference on Machine Learning and Knowledge Discovery in Databases.

[Paper]

For details, please see the original paper, or this brief explanation. A simple use case is provided in demo.ipynb

Embeddings are generated for a networkx graph through the get_embeddings function:

embeddings = get_embeddings(
    A, # networkx graph or numpy matrix
    S, # list of scales
    T, # list of sampling points
    q, # rotation parameter
    kernel, # a kernel function. Can be a custom function or lib.heat_kernel | low_pass_filter_kernel
    **kernel_args # parameters supplied to the kernel
)

An example using the same parameters as the authors, with an undirected and unweighted graph:

from lib import get_embeddings, low_pass_filter_kernel

import numpy as np
import networkx as nx

G = nx.karate_club_graph()
# parameters used in paper
S = np.arange(2.0, 20.1, 0.1) 
T = np.arange(1, 11, 1) 
q = 0.02
kernel = low_pass_filter_kernel
c = 2

embeddings = get_embeddings(
    A=G,
    S=S,
    T=T,
    q=q,
    kernel=kernel,
    c=2
)

See this youtube clip for a brief explanation of how GraphWave works - they use the graph Laplacian, which only works for undirected graphs and is replaced by the Hermitian Laplacian by Furutani et al.

See Wikipedia for an explanation of laplacian matrices