Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance
Abstract
In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observations in many domains. Further, in many cases the target entities for analysis are actually signals on such graphs. We propose to compare and organize such datasets of graph signals by using an earth mover's distance (EMD) with a geodesic cost over the underlying graph. Typically, EMD is computed by optimizing over the cost of transporting one probability distribution to another over an underlying metric space. However, this is inefficient when computing the EMD between many signals. Here, we propose an unbalanced graph EMD that efficiently embeds the unbalanced EMD on an underlying graph into an $L^1$ space, whose metric we call unbalanced diffusion earth mover's distance (UDEMD). Next, we show how this gives distances between graph signals that are robust to noise. Finally, we apply this to organizing patients based on clinical notes, embedding cells modeled as signals on a gene graph, and organizing genes modeled as signals over a large cell graph. In each case, we show that UDEMDbased embeddings find accurate distances that are highly efficient compared to other methods.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 DOI:
 10.48550/arXiv.2107.12334
 arXiv:
 arXiv:2107.12334
 Bibcode:
 2021arXiv210712334T
 Keywords:

 Computer Science  Machine Learning;
 Electrical Engineering and Systems Science  Signal Processing
 EPrint:
 5 pages, 5 figures, ICASSP 2022