Abstract Existing hashing methods can hardly realize the approximate mapping of the original feature space quickly.Therefore,a hashing method based on wavelet projection is proposed.Firstly,the projection matrix is constructed based on Haar wavelet transform.The projection matrix is optimized iteratively and binary codes are optimized by discrete method to control the quantization error.Then,the projection matrix is utilized to project the original feature vector of the image into the low-dimensional space quickly and binary codes are obtained by binary embedding.Experimental results on image datasets demonstrate that the proposed method improves encoding efficiency effectively.
[1] 文庆福,王建民,朱 晗.面向近似近邻查询的分布式哈希学习方法.计算机学报,2017,40(1):192-206. (WEN Q F,WANG J M,ZHU H.Distributed Learning to Hash for Approximate Nearest Neighbor Search.Chinese Journal of Compu-ters,2017,40(1):192-206.) [2] DATAR M,IMMORLICA N,INDYK P, et al.Locality-Sensitive Hashing Scheme Based on P-Stable Distributions//Proc of the 20th Annual Symposium on Computational Geometry.New York,USA:ACM,2004:253-262. [3] RAGINSKY M,LAZEBNIK S.Locality-Sensitive Binary Codes from Shift-Invariant Kernels//BENGIO Y,SCHUURMANS D,LAFFERTY J D,et al.,eds.Advances in Neural Information Processing Systems 22.Cambridge,USA:The MIT Press,2009:1509-1517. [4] KULIS B,GRAUMAN K.Kernelized Locality-Sensitive Hashing for Scalable Image Search//Proc of the 12th IEEE International Conference on Computer Vision.Washington,USA:IEEE,2009:2130-2137. [5] KULIS B,JAIN P,GRAUMAN K.Fast Similarity Search for Lear-ned Metrics.IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(12):2143-2157. [6] GONG Y C,LAZEBNIK S,GORDO A,et al.Iterative Quantization:A Procrustean Approach to Learning Binary Codes for Large-scale Image Retrieval.IEEE Transactions on Pattern Analysis and Machine Intelligence,2013,35(12):2916-2929. [7] WEISS Y,TORRALBA A,FERGUS R.Spectral Hashing//Proc of the 21st International Conference on Neural Information Processing Systems.Cambridge,USA:The MIT Press,2008:1753-1760. [8] JIANG Q Y,CUI X,LI W J.Deep Discrete Supervised Hashing.IEEE Transactions on Image Processing,2018,27(12):5996-6009. [9] 李武军,周志华.大数据哈希学习:现状与趋势.科学通报,2015,60(5/6):485-490. (LI W J,ZHOU Z H.Learning to Hash for Big Data:Current Status and Future Trends.Chinese Science Bulletin,2015,60(5/6):485-490.) [10] LIU W,MU C,KUMAR S,et al. Discrete Graph Hashing//GHAHAHRAMANI Z,WELLING M,CORTES C,et al.,eds.Advances in Neural Information Processing Systems 27.Cambridge,USA:The MIT Press,2014:3419-3427. [11] GONG Y C,KUMAR S,ROWLEY H A,et al. Learning Binary Codes for High-Dimensional Data Using Bilinear Projections//Proc of the IEEE Conference on Computer Vision and Pattern Re-cognition.Washington,USA:IEEE,2013:484-491. [12] SHEN F M,SHEN C H,LIU W,et al.Supervised Discrete Ha-shing//Proc of the IEEE Conference on Computer Vision and Pa-ttern Recognition.Washington,USA:IEEE,2015:37-45. [13] GUI J,LIU T L,SUN Z N,et al.Fast Supervised Discrete Ha-shing.IEEE Transactions on Pattern Analysis and Machine Intelligence,2018,40(2):490-496. [14] LAI Z H,CHEN Y D,WU J,et al. Jointly Sparse Hashing for Image Retrieval.IEEE Transactions on Image Processing,2018,27(12):6147-6158. [15] MA L,LI H L,MENG F M,et al.Discriminative Deep Metric Learning for Asymmetric Discrete Hashing.Neurocomputing,2020,380:115-124. [16] JOHNSON W B,LINDENSTRAUSS J.Extensions of Lipschitz Mappings into a Hilbert Space.Contemporary Mathematics,1984,26(1):189-206. [17] AILON N,CHAZELLE B.Approximate Nearest Neighbors and the Fast Johnson-Lindenstrauss Transform//Proc of the 38th Annual ACM Symposium on Theory of Computing.New York,USA:ACM,2006:557-563. [18] AILON N,LIBERTY E.An Almost Optimal Unrestricted Fast Johnson-Lindenstrauss Transform.ACM Transactions on Algorithms,2013,9(3).DOI:10.1145/2483699.2483701. [19] AGAIAN S S,SARUKHANYAN H G,EGIAZARIAN K O,et al. Hadamard Transforms.Bellingham,USA:SPIE,2011. [20] CHEON G S,SHADER B L.Sparse Orthogonal Matrices and the Haar Wavelet.Discrete Applied Mathematics,2000,101(1/2/3):63-76. [21] XIA Y,HE K M,KOHLI P,et al. Sparse Projections for High-Dimensional Binary Codes//Proc of the IEEE Conference on Computer Vision and Pattern Recognition.Washington,USA:IEEE, 2015:3332-3339. [22] HONG W X,YUAN J S.Fried Binary Embedding:From High-Dimensional Visual Features to High-Dimensional Binary Codes.IEEE Transactions on Image Processing,2018,27(10):4825-4837. [23] COURANT R.Variational Methods for the Solution of Problems of Equilibrium and Vibrations.Bulletin of the American Mathematical Society,1943,49(1):1-24. [24] ZHANG K,ZUO W M,GU S H,et al. Learning Deep CNN Denoiser Prior for Image Restoration//Proc of the IEEE Conference on Computer Vision and Pattern Recognition.Washington,USA:IEEE,2017:2808-2817. [25] WANG Y L,YANG J F,YIN W T,et al.A New Alternating Minimization Algorithm for Total Variation Image Reconstruction.SIAM Journal on Imaging Sciences,2008,1(3):248-272. [26] GOWER J C,DIJKSTERHUIS G B.Procrustes Problems.Oxford,UK:Oxford University Press,2004. [27] NOCEDAL J,WRIGHT S J.Sequential Quadratic Programming.Berlin,Germany:Springer,2006. [28] MA L,LI H L,MENG F M,et al.Learning Efficient Binary Codes from High-Level Feature Representations for Multilabel Image Retrieval.IEEE Transactions on Multimedia,2017,19(11):2545-2560. [29] LU X,ZHU L,CHENG Z Y,et al. Efficient Discrete Latent Semantic Hashing for Scalable Cross-Modal Retrieval.Signal Proce-ssing,2019,154:217-231. [30] KONG W H,LI W J.Isotropic Hashing//PEREIRA F,BURGES C J C,BOTTOU L,et al.,eds.Advances in Neural Information Processing Systems 25.Cambridge,USA:The MIT Press,2012:1646-1654. [31] YU F X,BHASKARA A,KUMAR S,et al.On Binary Embe-dding Using Circulant Matrices.Journal of Machine Learning Research,2018,18:1-30.
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