Differentiable Distance Between Hierarchically-Structured Data
Keywords: Distance, Distance function, Tree-structured data, Heterogenous Graphs, JSONs, Multiple Instance Learning
Abstract: Many machine learning algorithms solving various problems are available for
metric spaces. While there are plenty of distances for vector spaces, much
less exists for structured data (rooted heterogeneous trees) stored in popular
formats like JSON, XML, ProtoBuffer, MessagePack, etc. This paper
introduces the Hierarchically-structured Tree Distance (HTD) designed
especially for these data. The HTD distance is modular with differentiable
parameters weighting the importance of different sub-spaces. This allows
the distance to be tailored to a given dataset and task, such as classification,
clustering, and anomaly detection. The extensive experimental comparison
shows that distance-based algorithms with the proposed HTD distance
are competitive to state-of-the-art methods based on neural networks with
orders of magnitude more parameters. Furthermore, we show that HTD is
more suited to analyze heterogeneous Graph Neural Networks than Tree
Mover’s Distance.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 7973
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