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Pattern Recognition 78 (2018) 79–90
Contents lists available at ScienceDirect
Pattern Recognition
journal homepage: www.elsevier.com/locate/patcog
Supervised discrete discriminant hashing for image retrieval
Yan Cui a , d , ∗, Jielin Jiang
b , d , Zhihui Lai c , d , Zuojin Hu
a , WaiKeung Wong
d , ∗
a School of Mathematics and Information Science, Nanjing Normal University of Special Education, Nanjing, 210038, China b School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China c College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, 518060, China d Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong, China
a r t i c l e i n f o
Article history:
Received 13 August 2017
Revised 18 November 2017
Accepted 7 January 2018
Available online 11 January 2018
Keywords:
Supervised hash learning
Discrete hash learning
Discrete hash codes
Discriminant information
Robust similarity metric
a b s t r a c t
Most existing hashing methods usually focus on constructing hash function only, rather than learning dis-
crete hash codes directly. Therefore the learned hash function in this way may result in the hash function
which can-not achieve ideal discrete hash codes. To make the learned hash function for achieving ideal
approximated discrete hash codes, in this paper, we proposed a novel supervised discrete discriminant
hashing learning method, which can learn discrete hashing codes and hashing function simultaneously.
To make the learned discrete hash codes to be optimal for classification, the learned hashing framework
aims to learn a robust similarity metric so as to maximize the similarity of the same class discrete hash
codes and minimize the similarity of the different class discrete hash codes simultaneously. The discrim-
inant information of the training data can thus be incorporated into the learning framework. Meanwhile,
the hash functions are constructed to fit the directly learned binary hash codes. Experimental results
clearly demonstrate that the proposed method achieves leading performance compared with the state-
iscrete hashing learning methods, SDH achieves 36.05% on 32 bit
ode length and FSDH achieves 36.13% on 16 bit code length; com-
ared with the best performance of others non-discrete hashing
ethods, LSH achieves 14.08% on 32 bit code length, ITQ achieves
4.55% on 32 bit length and KSH achieves 28.52% on 64 bit code
ength. For the recall of Hamming radius 2, the proposed SDDH
chieves 99.78%, compared with 82.23% for LSH, 82.49% for ITQ,
4.24% for KSH, 99.53% for SDH and 99.52% for FSDH. For the F-
easure, the proposed SDDH is superior to all other non-discrete
ashing learning methods and slightly outperforms the discrete
ashing learning methods SDH and FSDD. For the hamming rank
ndex, the MAP of the proposed SDDH is slightly superior to all
ther hashing learning methods. To better illustrate the effective-
ess of the proposed SDDH, we further compared the training time
nd the testing time of these hashing learning methods and the
etails can be found in the Fig. 3 .
From Fig. 3 , we can see that the training time of the proposed
DDH is significantly shorter than KSH, similar to LSH, ITQ, FSDH.
ith increasing the code length, the training time of KSH and SDH
s increased quickly while the training of other hashing methods
s changed slightly. however with increasing the code length, the
esting time of SDH, FSDH and the proposed SDDH is increased
uickly. Thus the timeliness of the proposed SDDH is poorer than
ther hashing methods to some extent.
.4. Experiments on AR dataset
To expend the variety of data, we applied the proposed SDDH
n AR face data, and compares the proposed SDDH with other
ashing methods. The AR database consists of over 40 0 0 frontal
mages for 126 individuals. For each individual, 26 pictures were
aken in two separate sessions [49] . These images include more
acial variations, including illumination change, expressions, and
acial disguises. In our experiment, every class data set was ran-
omly split into a training set and test set at a ratio of 5:2. For
SH, SDH and FSDH, we randomly selected 500 samples as an-
hor points. The performance of the proposed SDDH was evalu-
ted in precision, recall, and F-measure of Hamming radius 2 and
AP, and compared against that of LSH, ITQ, AGH, KSH, SDH, and
SDH in as well. Experimental results on NUS-WIDE are shown in
able 4 .
From Table 4 , it is found that the proposed SDDH outperforms
ll other hashing methods. When the code length is 16, the pro-
osed SDDH achieves best performance. Specifically, the precision
ate is 43.03%, compared with 41.75% for SDH and 37.97% for FSDH,
nd significantly higher than LSH, ITQ, AGH and KSH. When the
ode length is 16, the recall rate of the proposed SDDH is 48.12%,
ompared with 33.52% for AGH, 40.00% for SDH and 38.19% for
SDH, and obviously outperform LSH, ITQ and KSH. The F-feature
88 Y. Cui et al. / Pattern Recognition 78 (2018) 79–90
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of the proposed SDDH is 45.43% and the MAP is 0.7338, which
outperform all other hashing methods. Furthermore, we compared
the training and testing time of the proposed SDDH with LSH, ITQ,
AGH, KSH, SDH and FSDH. From Table 5 , we know that the train-
ing time of the proposed SDDH is similar to FSDH, and the testing
time is similar to SDH and FSDH. The training time of KSH is much
higher than the proposed SDDH and other methods.
4.5. Discussion
We evaluate the effectiveness of the proposed SDDH on CIFAR-
10, MNIST and NUS-WIDE and AR face datasets. Form the results
of the experiments, it is clear that the performance of SDDH out-
performs the data-independent hashing methods LSH, the unsu-
pervised hashing methods ITQ KMH, ABQ and AHG, and the super-
vised hashing methods KSH, SDH and FSDH. For CIFAR-10 dataset,
the proposed SDDH achieves better performance in hash lookup
index (precision, recall and F-measure), while the performance of
the hamming ranking MAP index is similar to SDH and FSDH, but
obviously higher than LSH, ITQ, KMH, ABQ, AGH and KSH. For the
MNIST dataset, the proposed SDDH slightly outperforms KSH, SDH
and FSDH in precision and MAP index, while is obviously supe-
rior to LSH, ITQ, KMH, ABQ and AGH. For NUS-WIDE and AR face
datasets, the proposed SDDH outperforms all other methods as
well though the advantage of efficiency is not highlighted. For SDH
and FSDH, the proposed learning frameworks use l 2 loss function
for the classification model, the l 2 loss function is mainly used to
measure the loss between the learned hash bits and class labels
vector, the l 2 loss function may be more reasonable for multi-class
labels databases. In comparing with SDH and FSDH, the proposed
SDDH enhances the discriminant of the training data by maxi-
mizing the similarity of the same class samples and minimizing
the similarity of the different class samples simultaneously, which
is effective for single-class label and multi-class labels databases.
In contrast to the state-of-the-art hashing methods, the proposed
SDDH can incorporate the label information into the hash code
learning, update the directly learned hash codes in each iteration
and achieve the optimal hashing function from the directly learned
discrete hash codes.
5. Conclusions
In this paper, we propose the supervised discrete discriminant
hashing (SDDH). To utilize the label information of the training
data, a robust learned distance metric is used to make the binary
bits of the same class samples more similar, and the binary bits
of the different class samples more dissimilar, such that the dis-
criminant information of the training data can be incorporated into
the learning framework. Meanwhile, let the learned hash function
achieve optimal approximate discrete hash codes, a hash functions
learned regular term is embedded in the proposed supervised dis-
crete discriminant hashing framework, which make the hash func-
tions to be optimized based on the directly learned discrete hash
codes. Meanwhile, such learned hashing function is optimal for the
testing data. Therefore, the proposed supervised discrete discrim-
inant hashing incorporates the discrete binary bits learning and
hashing functions learning into an integrated framework, which
make the SDDH framework more practical in the real-world ap-
plications. Furthermore, the experimental results show that the ef-
ficacy of the proposed SDDH for large-scale image retrieval.
Acknowledgments
The authors would like to thank the editor and the anony-
mous reviewers for their critical and constructive comments and
suggestions. This work is supported by the National Science
oundation of China (Grant no. 61601235 , 61573248 , 61773328 ,
1732011 ), the Natural Science Foundation of Jiangsu Province
f China (Grant no. BK20170768 , BK20160972 ), the Natural Sci-
nce Foundation of the Jiangsu Higher Education Institutions of
hina (Grant no. 17KJB520 019, 16KJB520 031), the Startup Foun-
ation for Introducing Talent of Nanjing University of Informa-
ion Science and Technology (Grant no. 2243141601019), the Shen-
hen Municipal Science and Technology Innovation Council (Grant
o. JCYJ20170302153434048), the Natural Science Foundation of
uangdong Province (Grant no. 2017A030313367) and a Research
rant of the Hong Kong Polytechnic University (Project code:
-ZZDR ).
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90 Y. Cui et al. / Pattern Recognition 78 (2018) 79–90
ng University, Liaocheng, China, in 2008 and 2011, respectively. She received her Ph.D.
logy, on the subject of pattern recognition and intelligence systems in 2015. She visited niversity of Miami, USA, from May 2013 to November, 2013; She is currently working as
g, Hong Kong Polytechnic University. She is a lecturer in the College of Mathematics and
l Education. Her current research interests include pattern recognition, machine learning
al University, Huainan, China in 2007. He received the M.S. degree from Inner Mongolia
om the Nanjing University of Science and Technology, on the subject of pattern recog- 013 to August 2013, he was an Exchange Student with the Department of Computing,
he is a lecturer in the School of Computer and Software, Jiangsu Engineering Center of ience and Technology. His current research interests include image denoising and image
South China Normal University, M.S degree from Jinan University, and the Ph.D. degree
g University of Science and Technology (NUST), China, in 20 02, 20 07 and 2011, respec- ral Fellow from 2010 to 2013 at The Hong Kong Polytechnic University. Currently, he is
Shenzhen Graduate School, Harbin Institute of Technology (HIT). His research interests ased image retrieval, pattern recognition, compressive sense, human vision modelization
.
ion and intelligence system from Nanjing university of Science and Technology (NUST), atics and Information Science, Nanjing Normal University of Special Education, Nanjing
tern recognition, computer vision, face recognition, facial expression analysis and content-
g Kong Polytechnic University. Currently, he is an associate professor in this university. fereed journals, including IEEE Transactions on Neural Networks and Learning Systems,
conomics, European Journal of Operational Research, International Journal of Production tems, Man, and Cybernetics, among others. His recent research interests include artificial
timization of manufacturing scheduling, planning and control.
Yan Cui received her B.S. and M.S. degree from Liaoche
degree from the Nanjing University of Science and Technothe Department of Electrical and Computer Engineering, U
a research assistant at the Institute of Textiles and Clothin
Information Science, Nanjing Normal University of Speciaand image retrieval.
Jielin Jiang received the B.S. degree from Huainan Norm
University of Technology in 2010 and the Ph.D. degree frnition and intelligence systems in 2015. From February 2
the Hong Kong Polytechnic University, Hong Kong. Now, Network Monitoring, Nanjing University of Information Sc
classification.
Zhihui Lai received the B.S degree in mathematics from
inpattern recognition and intelligence system from Nanjintively. He has been a research associate and a Postdocto
a Postdoctoral Fellow at Bio-Computing Research Center,include face recognition, image processing and content-b
and applications in the fields of intelligent robot research
Zuojin Hu received the Ph.D. degree in pattern recognitNanjing, China. He is a professor in the College of Mathem
210038, China. His current interests are in the areas of pat
based image retrieval.
Waikeung Wong received his Ph.D. degree from The HonHe has published more than fifty scientific articles in re
Pattern Recognition, International Journal of Production EResearch, Computers in Industry, IEEE Transactions on Sys
intelligence, pattern recognition, feature extraction and op