learning based on sparse representation and real-world appli-
cations such as image processing, image classification, and
visual tracking.

Sparse representation has become a fundamental tool, which
has been embedded into various learning systems and also has
received dramatic improvements and unprecedented achieve-
ments. Furthermore, dictionary learning is an extremely pop-
ular topic and is closely connected with sparse representa-
tion. Currently, efficient sparse representation, robust sparse
representation, and dictionary learning based on sparse rep-
resentation seem to be the main streams of research on
sparse representation methods. The low-rank representation
technique has also recently aroused intensive research interests
and sparse representation has been integrated into low-rank
representation for constructing more reliable representation
models. However, the mathematical justification of low-rank
representation seems not to be elegant as sparse representation.
Because employing the ideas of sparse representation as a
prior can lead to state-of-the-art results, incorporating sparse
representation with low-rank representation is worth further
research. Moreover, subspace learning also has been becoming
one of the most prevailing techniques in pattern recognition
and computer vision. It is necessary to further study the rela-
tionship between sparse representation and subspace learning,
and constructing more compact models for sparse subspace
learning becomes one of the popular topics in various research
fields. The transfer learning technique has emerged as a new
learning framework for classification, regression and clustering
problems in data mining and machine learning. However,
sparse representation research still has been not fully applied to
the transfer learning framework and it is significant to unify the
sparse representation and low-rank representation techniques
into the transfer learning framework to solve domain adaption,
multitask learning, sample selection bias and covariate shift
problems. Furthermore, researches on deep learning seems
to become an overwhelming trend in the computer vision
field. However, dramatically expensive training effort is the
main limitation of current deep learning technique and how to
fully introduce current sparse representation methods into the
framework of deep learning is valuable and unsolved.

The application scope of sparse representation has emerged
and has been widely extended to machine learning and
computer vision fields. Nevertheless, the effectiveness and
efficiency of sparse representation methods cannot perfectly
meet the need for real-world applications. Especially, the
complexities of sparse representation have greatly affected
the applicability, especially the applicability to large scale
problems. Enhancing the robustness of sparse representation is
considered as another indispensable problem when researchers
design algorithms. For image classification, the robustness
should be seriously considered, such as the robustness to
random corruptions, varying illuminations, outliers, occlusion
and complex backgrounds. Thus, developing an efficient and
robust sparse representation method for sparse representation
is still the main challenge and to design a more effective dic-
tionary is being expected and is beneficial to the performance
improvement.

Sparse representation still has wide potential for various

possible applications, such as event detection, scene recon-
struction, video tracking, object recognition, object pose es-
timation, medical image processing, genetic expression and
natural language processing. For example, the study of sparse
representation in visual tracking is an important direction and
more depth studies are essential to future further improvements
of visual tracking research.

In addition, most sparse representation and dictionary learn-
ing algorithms focus on employing the l₀-norm or l₁-norm
regularization to obtain a sparse solution. However, there are
still only a few studies on l₂,₁-norm regularization based sparse
representation and dictionary learning algorithms. Moreover,
other extended studies of sparse representation may be fruitful.
In summary, the recent prevalence of sparse representation
has extensively influenced different fields. It is our hope
that the review and analysis presented in this paper can
help and motivate more researchers to propose perfect sparse
representation methods.

ACKNOWLEDGMENT

This work was supported in part by the National Nat-
ural Science Foundation of China under Grant 61370163,
Grant 61233011, and Grant 61332011, and in part by
the Shenzhen Municipal Science and Technology Innova-
tion Council under Grant JCYJ20130329151843309, Grant
JCYJ20130329151843309, Grant JCYJ20140417172417174,
Grant CXZZ20140904154910774, the China Postdoctoral Sci-
ence Foundation funded project, No. 2014M560264 and the
Shaanxi Key Innovation Team of Science and Technology
(Grant no.: 2012KCT-04).

We would like to thank Jian Wu for many inspiring dis-
cussions and he is ultimately responsible for many of the
ideas in the algorithm and analysis. We would also like to
thank Dr. Zhihui Lai, Dr. Jinxing Liu and Xiaozhao Fang
for constructive suggestions. Moreover, we thank the editor,
an associate editor, and referees for helpful comments and
suggestions which greatly improved this paper.

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<figure><img src="image_11.png" /></figure>

**Zheng Zhang** received the B.S degree from Henan University of Science and Technology and M.S degree from Shenzhen Graduate School, Harbin Institute of Technology (HIT) in 2012 and 2014, respectively. Currently, he is pursuing the Ph.D. degree in computer science and technology at Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China. His current research interests include pattern recognition, machine learning and computer vision.

<figure><img src="image_12.png" /></figure>

**Yong Xu** was born in Sichuan, China, in 1972. He received his B.S. degree and M.S. degree at Air Force Institute of Meteorology (China) in 1994 and 1997, respectively. He received the Ph.D. degree in Pattern recognition and Intelligence System at the Nanjing University of Science and Technology (NUST) in 2005. Now, he works at Shenzhen Graduate School, Harbin Institute of Technology. His current interests include pattern recognition, biometrics, machine learning and video analysis.

<figure><img src="image_13.png" /></figure>

**Jian Yang** received the B.S. degree in mathematics from the Xuzhou Normal University in 1995. He received the M.S. degree in applied mathematics from the Changsha Railway University in 1998 and the Ph.D. degree from the Nanjing University of Science and Technology (NUST), on the subject of pattern recognition and intelligence systems in 2002. In 2003, he was a postdoctoral researcher at the University of Zaragoza. From 2004 to 2006, he was a Postdoctoral Fellow at Biometrics Centre of Hong Kong Polytechnic University. From 2006 to 2007, he was a Postdoctoral Fellow at Department of Computer Science of New Jersey Institute of Technology. Now, he is a professor in the School of Computer Science and Technology of NUST. He is the author of more than 80 scientific papers in pattern recognition and computer vision. His journal papers have been cited more than 1600 times in the ISI Web of Science, and 2800 times in the Web of Scholar Google. His research interests include pattern recognition, computer vision and machine learning. Currently, he is an associate editor of Pattern Recognition Letters and IEEE TRANSACTION ON NEURAL NETWORKS AND LEARNING SYSTEMS, respectively.

**Xuelong Li** is a Full Professor with the Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi'an 710119, Shaanxi, P.R. China.
<figure><img src="image_14.png" /></figure>

**David Zhang** graduated in Computer Science from Peking University. He received his M.Sc. in Computer Science in 1982 and his Ph.D. in 1985 from the Harbin Institute of Technology (HIT). From 1986 to 1988 he was a Postdoctoral Fellow at Tsinghua University and then an Associate Professor at the Academia Sinica, Beijing. In 1994 he received his second Ph.D. in Electrical and Computer Engineering from the University of Waterloo, Ontario, Canada. Currently, he is a Chair Professor at the Hong Kong Polytechnic University where he is the Founding Director of the Biometrics Technology Centre (UGC/CRC) supported by the Hong Kong SAR Government in 1998. He also serves as Visiting Chair Professor in Tsinghua University, and Adjunct Professor in Shanghai Jiao Tong University, Peking University, Harbin Institute of Technology, and the University of Waterloo. He is the Founder and Editor-in-Chief, International Journal of Image and Graphics (IJIG); Book Editor, Springer International Series on Biometrics (KISB); Organizer, the first International Conference on Biometrics Authentication (ICBA); Associate Editor of more than ten international journals including IEEE Transactions and Pattern Recognition; Technical Committee Chair of IEEE CIS and the author of more than 10 books and 200 journal papers. Professor Zhang is a Croucher Senior Research Fellow, Distinguished Speaker of the IEEE Computer Society, and a Fellow of both IEEE and IAPR.