# Semi-supervised Kernel Metric Learning Using Relative Comparisons

Source: [Semi-supervised Kernel Metric Learning Using Relative Comparisons](<https://www.sota2.com/research/paper/68fa62fe1e209131ce9fc125>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T20:30:18.740Z

Authors: Ehsan Amid, Aristides Gionis, Antti Ukkonen

Published: 2016-12-01T00:16:53.000Z

## Abstract

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors of the data items. The relative-distance constraints used in this work are particularly effective in expressing structures at finer level of detail than must-link (ML) and cannot-link (CL) constraints, which are most commonly used for semi-supervised clustering. Relative-distance constraints are thus useful in settings where providing an ML or a CL constraint is difficult because the granularity of the true clustering is unknown.   Our main contribution is an efficient algorithm for learning a kernel matrix using the log determinant divergence --- a variant of the Bregman divergence --- subject to a set of relative-distance constraints. The learned kernel matrix can then be employed by many different kernel methods in a wide range of applications. In our experimental evaluations, we consider a semi-supervised clustering setting and show empirically that kernels found by our algorithm yield clusterings of higher quality than existing approaches that either use ML/CL constraints or a different means to implement the supervision using relative comparisons.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Unsupervised character discovery on Omniglot cross-task from bg (eval)](<https://www.sota2.com/research/sota/unsupervised-character-discovery-on-omniglot-cross-task-from-bg-eval.md>): Unsupervised character discovery; Omniglot cross-task from bg (eval); Accuracy (100): 0.468.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1612.00086>)

[PDF](<https://arxiv.org/pdf/1612.00086.pdf>)