{"type":"ScholarlyArticle","title":"RHash: Robust Hashing via L_infinity-norm Distortion","authors":[{"name":"Amirali Aghazadeh","slug":"amirali-aghazadeh","given":"Amirali","family":"Aghazadeh","affiliation":"Rice University , Houston , TX , USA"},{"name":"Andrew Lan","slug":"andrew-lan","given":"Andrew","family":"Lan","affiliation":"Princeton University , Princeton , NJ , USA"},{"name":"Anshumali Shrivastava","slug":"anshumali-shrivastava","given":"Anshumali","family":"Shrivastava","affiliation":"Rice University , Houston , TX , USA"},{"name":"Richard Baraniuk","slug":"richard-baraniuk","given":"Richard","family":"Baraniuk","affiliation":"Rice University , Houston , TX , USA"}],"abstract":"Hashing is an important tool in large-scale machine learning. Unfortunately, current data-dependent hashing algorithms are not robust to small perturbations of the data points, which degrades the performance of nearest neighbor (NN) search. The culprit is the minimization of the L_2-norm, average distortion among pairs of points to find the hash function. Inspired by recent progress in robust optimization, we develop a novel hashing algorithm, dubbed RHash, that instead minimizes the L_1-norm, worst-case distortion among pairs of points. We develop practical and efficient implementations of RHash that couple the alternating direction method of multipliers (ADMM) framework with column generation to scale well to large datasets. A range of experimental evaluations demonstrate the superiority of RHash over ten state-of-the-art binary hashing schemes. In particular, we show that RHash achieves the same retrieval performance as the state-of-the-art algorithms in terms of average precision while using up to 60% fewer bits.","doi":"10.24963/ijcai.2017/192","url":"https://ijcai.org/proceedings/2017/192","pdf":"https://ijcai.org/proceedings/2017/0192.pdf","markdown":"https://ijcai.org/proceedings/2017/192.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/192","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra, IIIA-CSIC","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":192,"pages":{"first":1386,"last":1394},"keywords":["Machine Learning: Machine Learning","Natural Language Processing: Information Retrieval"],"videos":[],"references":[{"position":1,"raw":"[Boyd et al., 2011] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipli- ers. Found. Trends Mach. Learn., 3(1):1-122, Jan. 2011.","title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","authors":"S Boyd, N Parikh, E Chu, B Peleato, J Eckstein","year":"2011","venue":"Found. Trends Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Chatterjee and Hadi, 2009] S. Chatterjee and A. S. Hadi. Sensitivity Analysis in Linear Regression, volume 327.","title":"Sensitivity Analysis in Linear Regression","authors":"S Chatterjee, A S Hadi","year":null,"venue":null,"doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Dantzig and Wolfe, 1960] G. B. Dantzig and P. Wolfe. De- composition principle for linear programs. Operations Re- search, 8(1):101-111, Feb. 1960.","title":"Decomposition principle for linear programs","authors":"G B Dantzig, P Wolfe","year":"1960","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Datar et al., 2004] M. Datar, N. Immorlica, P. Indyk, and V. S. Mirrokni. Locality-sensitive hashing scheme based on p-stable distributions. In Proc. Annu. Symp. Comput. Geometry, pages 253-262, June 2004.","title":"Locality-sensitive hashing scheme based on p-stable distributions","authors":"M Datar, N Immorlica, P Indyk, V S Mirrokni","year":"2004","venue":"Proc. Annu. Symp. Comput. Geometry","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Du and Pardalos, 2013] D. Du and P. M. Pardalos. Minimax and Applications, volume 4. Springer, 2013.","title":"Minimax and Applications","authors":"D Du, P M Pardalos","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Hartley and Schaffalitzky, 2004] R. Hartley and F. Schaffal- itzky. L ∞ minimization in geometric reconstruction prob- lems. In Proc. Conf. Comput. Vision Pattern Recogn. (CVPR), pages 504-509, June 2004.","title":"L ∞ minimization in geometric reconstruction problems","authors":"R Hartley, F Schaffalitzky","year":"2004","venue":"Proc. Conf. Comput. Vision Pattern Recogn. (CVPR)","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[He et al., 2012] J. He, S. Kumar, and S. Chang. On the diffi- culty of nearest neighbor search. In Proc. Int. Conf. Mach. Learn., pages 1127-1134, June 2012.","title":"On the difficulty of nearest neighbor search","authors":"J He, S Kumar, S Chang","year":"2012","venue":"Proc. Int. Conf. Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hegde et al., 2015] C. Hegde, A. C. Sankaranarayanan, W. Yin, and R. G. Baraniuk. Numax: A convex approach for learning near-isometric linear embeddings. IEEE Trans. Signal Process., 63(22):6109-6121, Nov. 2015.","title":"Numax: A convex approach for learning near-isometric linear embeddings","authors":"C Hegde, A C Sankaranarayanan, W Yin, R G Baraniuk","year":"2015","venue":"IEEE Trans. Signal Process","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Heo et al., 2012] J. Heo, Y. Lee, J. He, S. Chang, and S. Yoon. Spherical hashing. In Proc. Conf. Comput. Vi- sion Pattern Recogn., pages 2957-2964, June 2012.","title":"Spherical hashing","authors":"J Heo, Y Lee, J He, S Chang, S Yoon","year":"2012","venue":"Proc. Conf. Comput. Vision Pattern Recogn","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Indyk and Motwani, 1998] P. Indyk and R. Motwani. Ap- proximate nearest neighbors: Towards removing the curse of dimensionality. In Proc. Annu. Symp. Theory Comput., pages 604-613, May 1998.","title":"Approximate nearest neighbors: Towards removing the curse of dimensionality","authors":"P Indyk, R Motwani","year":"1998","venue":"Proc. Annu. Symp. Theory Comput","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Jégou et al., 2012] H. Jégou, T. Furon, and J. Fuchs. Anti- sparse coding for approximate nearest neighbor search. In Proc. Intl. Conf. Acoustics Speech Signal Process. (ICASSP), pages 2029-2032. IEEE, 2012.","title":"Antisparse coding for approximate nearest neighbor search","authors":"H Jégou, T Furon, J Fuchs","year":"2012","venue":"Proc. Intl. Conf. Acoustics Speech Signal Process. (ICASSP)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Jiang and Li, 2015] Q. Y. Jiang and W. J. Li. Scalable graph hashing with feature transformation. In Proc Intl. Joint Conf. Artif. Intell., Sep. 2015.","title":"Scalable graph hashing with feature transformation","authors":"Q Y Jiang, W J Li","year":"2015","venue":"Proc Intl. Joint Conf. Artif. Intell","doi":null,"url":null,"internal_url":"/proceedings/2015/318"},{"position":13,"raw":"[Kong and Li, 2012] W. Kong and W. Li. Isotropic hashing. In Adv. Neural Info. Process. Syst., pages 1646-1654, Dec. 2012.","title":"Isotropic hashing","authors":"W Kong, W Li","year":"2012","venue":"Adv. Neural Info. Process. Syst","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kulis and Darrell, 2009] B. Kulis and T. Darrell. Learning to hash with binary reconstructive embeddings. In Adv. Neural Inf. Process. Syst., pages 1042-1050, Dec. 2009.","title":"Learning to hash with binary reconstructive embeddings","authors":"B Kulis, T Darrell","year":"2009","venue":"Adv. Neural Inf. Process. Syst","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[LeCun and Cortes, 1998] Y. LeCun and C. Cortes. The MNIST database of handwritten digits, 1998.","title":"The MNIST database of handwritten digits","authors":"Y Lecun, C Cortes","year":"1998","venue":null,"doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Ledoux and Talagrand, 1991] M. Ledoux and M. Tala- grand. Probability in Banach Spaces: Isoperimetry and Processes. Springer-Verlag, 1991.","title":"Probability in Banach Spaces: Isoperimetry and Processes","authors":"M Ledoux, M","year":"1991","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Liu et al., 2011] W. Liu, J. Wang, S. Kumar, and S. Chang. Hashing with graphs. In Proc. Intl. Conf. Mach. Learn., pages 1-8, July 2011.","title":"Hashing with graphs","authors":"W Liu, J Wang, S Kumar, S Chang","year":"2011","venue":"Proc. Intl. Conf. Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Lowe, 2004] D. Lowe. Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision, 60(2):91-110, Nov. 2004.","title":"Distinctive image features from scale-invariant keypoints","authors":"D Lowe","year":"2004","venue":"Int. J. Comput. Vision","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Lv et al., 2007] Q. Lv, W. Josephson, Z. Wang, M. Charikar, and K. Li. Multi-probe lsh: efficient indexing for high- dimensional similarity search. In Proc. Int. Conf. Very Large databases, pages 950-961, Sep. 2007.","title":"Multi-probe lsh: efficient indexing for highdimensional similarity search","authors":"Q Lv, W Josephson, Z Wang, M Charikar, K Li","year":"2007","venue":"Proc. Int. Conf. Very Large databases","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Nesterov, 2007] Y. Nesterov. Gradient methods for mini- mizing composite objective function. Technical report, Université Catholique de Louvain, Sep. 2007.","title":"Gradient methods for minimizing composite objective function","authors":"Y Nesterov","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Norouzi and Fleet, 2011] M. Norouzi and D. J. Fleet. Min- imal loss hashing for compact binary codes. In Proc. Int. Conf. on Mach. Learn., pages 353-360, June 2011.","title":"Minimal loss hashing for compact binary codes","authors":"M Norouzi, D J Fleet","year":"2011","venue":"Proc. Int. Conf. on Mach. Learn","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Plan and Vershynin, 2014] Y. Plan and R. Vershynin. Di- mension reduction by random hyperplane tessellations. Discrete Comput. Geom., 51(2):438-461, Mar. 2014.","title":"Dimension reduction by random hyperplane tessellations","authors":"Y Plan, R Vershynin","year":"2014","venue":"Discrete Comput. Geom","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Snavely et al., 2006] N. Snavely, S. Seitz, and R. Szeliski. Photo tourism: Exploring photo collections in 3D. ACM Trans. Graphics, 25(3):835-846, July 2006.","title":"Photo tourism: Exploring photo collections in 3D","authors":"N Snavely, S Seitz, R Szeliski","year":"2006","venue":"ACM Trans. Graphics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Studer et al., 2014] C. Studer, T. Goldstein, W. Yin, and R. G. Baraniuk. Democratic representations. arXiv preprint arXiv:1401.3420, 2014.","title":"Democratic representations","authors":"C Studer, T Goldstein, W Yin, R G Baraniuk","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Torralba et al., 2008] A. Torralba, R. Fergus, and Y. Weiss. Small codes and large image databases for recognition. In Proc. Conf. Comput. Vision Pattern Recogn., pages 1-8, June 2008.","title":"Small codes and large image databases for recognition","authors":"A Torralba, R Fergus, Y Weiss","year":"2008","venue":"Proc. Conf. Comput. Vision Pattern Recogn","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wainwright, 2009] M. J. Wainwright. Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ 1 - constrained quadratic programming (Lasso). IEEE Trans. Info. Theory, 55(5):2183-2202, May 2009.","title":"Sharp thresholds for high-dimensional and noisy sparsity recovery using ℓ 1constrained quadratic programming (Lasso)","authors":"M J Wainwright","year":"2009","venue":"IEEE Trans. Info. Theory","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Wang et al., 2014] J. Wang, H. T. Shen, J. Song, and J. Ji. Hashing for similarity search: A survey. arXiv preprint arXiv:1408.2927, 2014.","title":"Hashing for similarity search: A survey","authors":"J Wang, H T Shen, J Song, J Ji","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Wang et al., 2016] Z. Wang, Y. Yang, S. Chang, Q. Ling, and T. S. Huang. Learning a deep ℓ ∞ encoder for hashing. In Proc. Intl. Joint Conf. Artif. Intell., pages 2174-2180. AAAI Press, 2016.","title":"Learning a deep ℓ ∞ encoder for hashing","authors":"Z Wang, Y Yang, S Chang, Q Ling, T S Huang","year":"2016","venue":"Proc. Intl. Joint Conf. Artif. Intell","doi":null,"url":null,"internal_url":"/proceedings/2016/310"},{"position":29,"raw":"[Weiss et al., 2009] Y. Weiss, A. Torralba, and R. Fergus. Spectral hashing. In Adv. Neural Inf. Process. Syst., pages 1753-1760, Dec. 2009.","title":"Spectral hashing","authors":"Y Weiss, A Torralba, R Fergus","year":"2009","venue":"Adv. Neural Inf. Process. Syst","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Weiss et al., 2012] Y. Weiss, R. Fergus, and A. Torralba. Multidimensional spectral hashing. In European Conf. Comput. Vision, pages 340-353, Oct. 2012.","title":"Multidimensional spectral hashing","authors":"Y Weiss, R Fergus, A Torralba","year":"2012","venue":"European Conf. Comput. Vision","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Wen et al., 2010] Z. Wen, W. Yin, D. Goldfarb, and Y. Zhang. A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. SIAM J. Sci. Comput., 32(4):1832-1857, June 2010.","title":"A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation","authors":"Z Wen, W Yin, D Goldfarb, Y Zhang","year":"2010","venue":"SIAM J. Sci. Comput","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Xu et al., 2009] H. Xu, C. Caramanis, and S. Mannor. Ro- bustness and regularization of support vector machines. J. Mach. Learn. Research, 10:1485-1510, 2009.","title":"Robustness and regularization of support vector machines","authors":"H Xu, C Caramanis, S Mannor","year":"2009","venue":"J. Mach. Learn. Research","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Yu et al., 2014] F. X. Yu, S. Kumar, Y. Gong, and S. Chang. Circulant binary embedding. In Proc. Int. Conf. Mach. Learn., pages 946-954, June 2014.","title":"Circulant binary embedding","authors":"F X Yu, S Kumar, Y Gong, S Chang","year":"2014","venue":"Proc. Int. Conf. Mach. Learn","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}