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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 379718, 10 pages
Research Article

Maximum Variance Hashing via Column Generation

1College of Computer, National University of Defense Technology, Changsha, Hunan 410073, China
2School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China
3School of Computer Science, The University of Adelaide, Adelaide, SA 5005, Australia

Received 23 January 2013; Accepted 6 March 2013

Academic Editor: Shengyong Chen

Copyright © 2013 Lei Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With the explosive growth of the data volume in modern applications such as web search and multimedia retrieval, hashing is becoming increasingly important for efficient nearest neighbor (similar item) search. Recently, a number of data-dependent methods have been developed, reflecting the great potential of learning for hashing. Inspired by the classic nonlinear dimensionality reduction algorithm—maximum variance unfolding, we propose a novel unsupervised hashing method, named maximum variance hashing, in this work. The idea is to maximize the total variance of the hash codes while preserving the local structure of the training data. To solve the derived optimization problem, we propose a column generation algorithm, which directly learns the binary-valued hash functions. We then extend it using anchor graphs to reduce the computational cost. Experiments on large-scale image datasets demonstrate that the proposed method outperforms state-of-the-art hashing methods in many cases.