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[2602.04192] LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data
Summary
The paper presents LORE, a framework for learning intrinsic dimensionality and ordinal embeddings from noisy triplet comparisons, enhancing perceptual modeling in machine learning.
Why It Matters
Understanding intrinsic dimensionality and similarity structures from ordinal data is crucial in fields like psychophysics and machine learning. LORE's approach allows for more interpretable models and efficient data usage, which can lead to advancements in how subjective perceptual spaces are analyzed.
Key Takeaways
- LORE learns both intrinsic dimensionality and ordinal embeddings simultaneously.
- It uses a nonconvex Schatten-$p$ quasi norm for regularization, eliminating the need for predefined embedding dimensions.
- The framework is optimized via an iteratively reweighted algorithm with established convergence guarantees.
- Extensive experiments demonstrate LORE's ability to recover latent geometries in subjective perceptual spaces.
- LORE opens new avenues for scalable discovery of low-dimensional structures from ordinal data.
Computer Science > Machine Learning arXiv:2602.04192 (cs) [Submitted on 4 Feb 2026 (v1), last revised 23 Feb 2026 (this version, v2)] Title:LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data Authors:Vivek Anand, Alec Helbling, Mark A. Davenport, Gordon J. Berman, Sankaraleengam Alagapan, Christopher John Rozell View a PDF of the paper titled LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data, by Vivek Anand and 5 other authors View PDF HTML (experimental) Abstract:Learning the intrinsic dimensionality of subjective perceptual spaces such as taste, smell, or aesthetics from ordinal data is a challenging problem. We introduce LORE (Low Rank Ordinal Embedding), a scalable framework that jointly learns both the intrinsic dimensionality and an ordinal embedding from noisy triplet comparisons of the form, "Is A more similar to B than C?". Unlike existing methods that require the embedding dimension to be set apriori, LORE regularizes the solution using the nonconvex Schatten-$p$ quasi norm, enabling automatic joint recovery of both the ordinal embedding and its dimensionality. We optimize this joint objective via an iteratively reweighted algorithm and establish convergence guarantees. Extensive experiments on synthetic datasets, simulated perceptual spaces, and real world crowdsourced ordinal judgements show that LORE learns compact, interpretable and highly accurate low di...