Abstract
With the growing availability of very large image databases, there has been a surge of interest in methods based on “semantic hashing”, i.e. compact binary codes of data-points so that the Hamming distance between codewords correlates with similarity. In reviewing and comparing existing methods, we show that their relative performance can change drastically depending on the definition of ground-truth neighbors. Motivated by this finding, we propose a new formulation for learning binary codes which seeks to reconstruct the affinity between datapoints, rather than their distances. We show that this criterion is intractable to solve exactly, but a spectral relaxation gives an algorithm where the bits correspond to thresholded eigenvectors of the affinity matrix, and as the number of datapoints goes to infinity these eigenvectors converge to eigenfunctions of Laplace-Beltrami operators, similar to the recently proposed Spectral Hashing (SH) method. Unlike SH whose performance may degrade as the number of bits increases, the optimal code using our formulation is guaranteed to faithfully reproduce the affinities as the number of bits increases. We show that the number of eigenfunctions needed may increase exponentially with dimension, but introduce a “kernel trick” to allow us to compute with an exponentially large number of bits but using only memory and computation that grows linearly with dimension. Experiments shows that MDSH outperforms the state-of-the art, especially in the challenging regime of small distance thresholds.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Gionis, A., Indyk, P., Motwani, R.: Similarity Search in High Dimensions via Hashing. In: Proc. Intl Conf. on Very Large Data Bases (1999)
Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In: FOCS, pp. 459–468 (2006)
Raginksi, M., Lazebnik, S.: Locality-sensitive binary codes from shift-invariant kernels. In: NIPS (2009)
Salakhutdinov, R.R., Hinton, G.E.: Semantic hashing. In: SIGIR Workshop on Information Retrieval and Applications of Graphical Models (2007)
Torralba, A., Fergus, R., Weiss, Y.: Small Codes and Large Image Databases for Recognition. In: CVPR (2008)
Weiss, Y., Torralba, A., Fergus, R.: Spectral hashing. In: NIPS (2008)
Xu, H., Wang, J., Li, Z., Zeng, G., Li, S., Yu, N.: Complementary hashing for approximate nearest neighbor search. In: ICCV, pp. 1631–1638 (2011)
Wang, J., Kumar, S., Chang, S.F.: Sequential projection learning for hashing with compact codes. In: ICML, pp. 1127–1134 (2010)
Kulis, B., Darrell, T.: Learning to Hash with Binary Reconstructive Embeddings. In: NIPS (2009)
Norouzi, M., Fleet, D.: Minimal loss hashing for compact binary codes. In: ICML (2011)
Lin, R., Yagnik, D.R.: Spec hashing: Similarity preserving algorithm for entropy-based coding. In: CVPR (2010)
Gong, Y., Lazebnik, S.: Iterative quantization: A procrustean approach to learning binary codes. In: CVPR (2011)
Srebro, N., Jaakkola, T.: Weighted low-rank approximations. In: ICML, pp. 720–727 (2003)
Kumar, S., Mohri, M., Talwalkar, A.: Sampling techniques for the Nystrom method. In: AISTATS (2009)
Coifman, R.R., Lafon, S., Lee, A., Maggioni, M., Nadler, B., Warner, F., Zucker, S.: Geometric diffusion as a tool for harmonic analysis and structure definition of data, part i: Diffusion maps. PNAS 21, 7426–7431 (2005)
Fergus, R., Weiss, Y., Torralba, A.: Semi-supervised learning in gigantic image collections. In: NIPS (2009)
Belkin, M., Niyogi, P.: Towards a theoretical foundation for laplacian-based manifold methods. J. Comput. Syst. Sci. 74, 1289–1308 (2008)
Nadler, B., Srebro, N., Zhou, X.: Statistical analysis of semi-supervised learning: The limit of infinite unlabelled data. In: NIPS, pp. 1330–1338 (2009)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE PAMI 22, 888–905 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Weiss, Y., Fergus, R., Torralba, A. (2012). Multidimensional Spectral Hashing. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33715-4_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-33715-4_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33714-7
Online ISBN: 978-3-642-33715-4
eBook Packages: Computer ScienceComputer Science (R0)