Large-Margin Metric Learning for Partitioning Problems

TL;DR

This paper introduces a large-margin metric learning approach for unsupervised partitioning tasks like clustering and segmentation, improving performance by learning a Mahalanobis metric from multiple datasets.

Contribution

It proposes a convex optimization framework for supervised metric learning tailored to various partitioning problems, enhancing accuracy through feature weighting and selection.

Findings

Learning the metric improves partitioning accuracy in synthetic data.

Enhanced segmentation performance in bioinformatics and image analysis.

Efficient convex optimization solves the large-margin structured prediction problem.

Abstract

In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the minimization of Euclidean distortions, which include mean-based change-point detection, K-means, spectral clustering and normalized cuts. Our main goal is to learn a Mahalanobis metric for these unsupervised problems, leading to feature weighting and/or selection. This is done in a supervised way by assuming the availability of several potentially partially labelled datasets that share the same metric. We cast the metric learning problem as a large-margin structured prediction problem, with proper definition of regularizers and losses, leading to a convex optimization problem which can be solved efficiently with iterative techniques. We provide experiments where we show how learning the metric may significantly improve the partitioning performance in synthetic examples, bioinformatics, video segmentation and image segmentation problems.