# Low-Rank Transfer Learning

## Abstract

Real-world visual data are expensive to label for the purpose of training supervised learning algorithms. Leverage of auxiliary databases with well labeled data for the new task may save considerable labeling efforts. However, data in the auxiliary databases are often obtained under conditions that differ from those in the new task. Transfer learning provides techniques for transferring learned knowledge from a *source* domain to a *target* domain by mitigating the divergence. In this chapter, we discuss transfer learning in a generalized subspace where each target sample can be represented by some combination of source samples under a low-rank constraint. Under this constraint, the underlying structure of both source and target domains are considered in the knowledge transfer, which brings in three benefits: First, good alignment between domains is ensured in that only relevant data in some subspace of the source domain are used to reconstruct the data in the target domain. Second, the discriminative power of the source domain is naturally passed on to the target domain. Third, noisy information will be filtered out in the knowledge transfer. Extensive experiments on synthetic data, and important computer vision problems, e.g., face recognition application, visual domain adaptation for object recognition, demonstrate the superiority of the proposed approach over the existing, well-established methods.

## Keywords

Transfer learning Low-rank constraint Subspace learning Domain adaptation## Notes

### Acknowledgments

This research is supported in part by the NSF CNS award 1314484, Office of Naval Research award N00014-12-1-1028, Air Force Office of Scientific Research award FA9550-12-1-0201, U.S. Army Research Office grant W911NF-13-1-0160, and IC Postdoc Program Grant 2011-11071400006.

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