Learning structured representations by embedding class hierarchy with fast optimal transport
Zeng, Siqi
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Permalink
https://hdl.handle.net/2142/129673
Description
Title
Learning structured representations by embedding class hierarchy with fast optimal transport
Author(s)
Zeng, Siqi
Issue Date
2025-04-21
Director of Research (if dissertation) or Advisor (if thesis)
Zhao, Han
Department of Study
Siebel School Comp & Data Sci
Discipline
Computer Science
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
hierarchical representation
representation learning
optimal transport
Abstract
To embed structured knowledge within labels into feature representations, prior work (Zeng et al., 2022) proposed to use the Cophenetic Correlation Coefficient (CPCC) as a regularizer during supervised learning. This regularizer calculates pairwise Euclidean distances of class means and aligns them with the corresponding shortest path distances derived from the label hierarchy tree. However, class means may not be good representatives of the class conditional distributions, especially when they are multi-mode in nature. To address this limitation, under the CPCC framework, we propose to use the Earth Mover's Distance (EMD) to measure the pairwise distances among classes in the feature space. We show that our exact EMD method generalizes previous work, and recovers the existing algorithm when class-conditional distributions are Gaussian in the feature space. To further improve the computational efficiency of our method, we introduce the Optimal Transport-CPCC family by exploring four EMD approximation variants. Our most efficient OT-CPCC variant runs in linear time in the size of the dataset, while maintaining competitive performance across datasets and tasks. The code is available at https://github.com/uiuctml/OTCPCC.
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