# LORE: Jointly Learning the Intrinsic Dimensionality and Relative Similarity Structure From Ordinal Data

arXiv: https://arxiv.org/abs/2602.04192 · HTML: https://mlsanity.com/paper/2602.04192/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 10 of 10)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Large language models predict human sensory judgments across six modalities](https://mlsanity.com/paper/2302.01308/) (2023)
- [A Similarity Measure for Material Appearance](https://mlsanity.com/paper/1905.01562/) (2019)
- [Cost-Effective HITs for Relative Similarity Comparisons](https://mlsanity.com/paper/1404.3291/) (2014)
- [Generalized Nonconvex Nonsmooth Low-Rank Minimization](https://mlsanity.com/paper/1404.7306/) (2014)
- [Finite Sample Prediction and Recovery Bounds for Ordinal Embedding](https://mlsanity.com/paper/1606.07081/) (2016)
- [Insights into Ordinal Embedding Algorithms: A Systematic Evaluation](https://mlsanity.com/paper/1912.01666/) (2019)
- [Active Ordinal Querying for Tuplewise Similarity Learning](https://mlsanity.com/paper/1910.04115/) (2019)
- [Lens depth function and k-relative neighborhood graph: versatile tools for ordinal data analysis](https://mlsanity.com/paper/1602.07194/) (2016)

## Abstract (arXiv)

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 dimensional embeddings that recover the latent geometry of subjective percepts. By simultaneously inferring both the intrinsic dimensionality and ordinal embeddings, LORE enables more interpretable and data efficient perceptual modeling in psychophysics and opens new directions for scalable discovery of low dimensional structure from ordinal data in machine learning.