# Less but Better: Generalization Enhancement of Ordinal Embedding via Distributional Margin

## TL;DR

This paper introduces a novel margin distribution learning approach called DMOE to improve the generalization of ordinal embedding, especially with limited comparison data, by optimizing margin distribution rather than just margin size.

## Contribution

The paper proposes a new paradigm for ordinal embedding that focuses on margin distribution, with a specific objective function and an efficient optimization algorithm, enhancing generalization with fewer samples.

## Key findings

- DMOE outperforms classical methods on simulated datasets.
- The approach improves embedding quality with limited comparison data.
- Experimental results validate the effectiveness of margin distribution optimization.

## Abstract

In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, collecting a large number of labeled data is known as a hard task, and most of the existing work pay little attention to the generalization ability with insufficient samples. Meanwhile, recent progress in large margin theory discloses that rather than just maximizing the minimum margin, both the margin mean and variance, which characterize the margin distribution, are more crucial to the overall generalization performance. To address the issue of insufficient training samples, we propose a margin distribution learning paradigm for ordinal embedding, entitled Distributional Margin based Ordinal Embedding (\textit{DMOE}). Precisely, we first define the margin for ordinal embedding problem. Secondly, we formulate a concise objective function which avoids maximizing margin mean and minimizing margin variance directly but exhibits the similar effect. Moreover, an Augmented Lagrange Multiplier based algorithm is customized to seek the optimal solution of \textit{DMOE} effectively. Experimental studies on both simulated and real-world datasets are provided to show the effectiveness of the proposed algorithm.