Metric Learning across Heterogeneous Domains by Respectively Aligning Both Priors and Posteriors

TL;DR

This paper introduces a novel metric learning approach that aligns priors and posteriors across heterogeneous domains by mapping samples into a common space, effectively handling domain differences with limited target labels.

Contribution

The work proposes a unified PSD matrix framework for aligning priors and posteriors in heterogeneous domain metric learning, with an efficient optimization algorithm and kernelization capability.

Findings

Effective in cross-language retrieval tasks.

Improves cross-domain object recognition accuracy.

Demonstrates robustness with limited target domain labels.

Abstract

In this paper, we attempts to learn a single metric across two heterogeneous domains where source domain is fully labeled and has many samples while target domain has only a few labeled samples but abundant unlabeled samples. To the best of our knowledge, this task is seldom touched. The proposed learning model has a simple underlying motivation: all the samples in both the source and the target domains are mapped into a common space, where both their priors P(sample)s and their posteriors P(label|sample)s are forced to be respectively aligned as much as possible. We show that the two mappings, from both the source domain and the target domain to the common space, can be reparameterized into a single positive semi-definite(PSD) matrix. Then we develop an efficient Bregman Projection algorithm to optimize the PDS matrix over which a LogDet function is used to regularize. Furthermore, we also show that this model can be easily kernelized and verify its effectiveness in crosslanguage retrieval task and cross-domain object recognition task.