1
Iterative Re-constrained Group Sparse Face
Recognition with Adaptive Weights Learning
Jianwei Zheng, Ping Yang, Shengyong Chen, Senior Member, IEEE,Guojiang Shen and Wanliang Wang
Abstract—In this paper, we consider the robust face recognition
problem via iterative re-constrained group sparse classifier with
adaptive weights learning (IRGSC). Specifically, we propose a
group sparse representation classification (GSRC) approach in
which weighted features and groups are collaboratively adopted
to encode more structure information and discriminative infor-
mation than other regression based methods. In addition, we
derive an efficient algorithm to optimize the proposed objective
function, and theoretically prove the convergence. There are sev-
eral appealing aspects associated with IRGSC. First, adaptively
learned weights can be seamlessly incorporated into the GSRC
framework. This integrates the locality structure of the data and
validity information of the features into l
2,p
-norm regularization
to form a unified formulation. Second, IRGSC is very flexible to
different size of training set as well as feature dimension thanks to
the l
2,p
-norm regularization. Third, the derived solution is proved
to be a stationary point (globally optimal if p≥1). Comprehensive
experiments on representative datasets demonstrate that IRGSC
is a robust discriminative classifier which significantly improves
the performance and efficiency compared with the state-of-the-
art methods in dealing with face occlusion, corruption, and
illumination changes, etc.
Index Terms—Sparse representation, classification, weights
learning, Group constraints, face recognition
I. INTRODUCTION
H
IGH sample dimensionality and short insufficiency of
prior knowledge about the valid features for classifica-
tion are two challenging problems in machine learning and
pattern recognition. Face recognition (FR) remains an active
topic after comprehensive research over the last two decades
not just owe to its great application potential [1], [2]. It
offers a good testbench to reveal how these two key machine
learning problems are solvable as large and unambiguous trial
databases are available for FR problem. Appearance based
method [3], also known as holistic method, which exploits
machine learning approaches on the complete image for both
feature selection and classification, provides a credible way
to cope with these two difficult machine learning problems.
However, robust FR w.r.t. occlusion/corruption is still an open
problem due to the variations of noises, such as real disguise,
This work was supported in part by the National Natural Science Foundation
of China under Grant Nos. 61602413, 61325019, U1509207, 61502424 and
61379123 and in part by the Zhejiang Provincial Natural Science Foundation
under Grant LY15F030014. (Corresponding author: Shengyong Chen.)
J. Zheng, P. Yang, G. Shen and W. Wang are with the college
of Computer Science and Technology, Zhejiang University of Technol-
ogy, Hangzhou 310023, China (e-mail: zjw@zjut.edu.cn; yizhongyang-
ping@126.com; gjshen1975@zjut.edu.cn; wwl@zjut.edu.cn).
S. Chen is with the college of Computer and Communication Engineering,
Tianjin University of Technology, Tianjin 300384, China, and also with
the college of Computer Science and Technology, Zhejiang University of
Technology, Hangzhou 310023, China (e-mail: csy@zjut.edu.cn).
continuous or pixel-wise occlusion, randomness of occlusion
position, and the percentage of occluded pixels.
Recently, regression analysis based approaches arouse broad
interests in FR community. Naseem et al. presented a linear
regression classifier (LRC) for FR [4], which represents the
query image by a linear combination of the class-specific dic-
tionary atoms. Wright et al. proposed a sparse representation
based classification (SRC) algorithm to identify face images
with different corruption and real disguise [5]. In SRC, a
query image is regressed as a sparse linear combination of
the dictionary atoms from all classes collaboratively, and then
the decision is made by identifying which subject yields the
minimal reconstruction residual. Both LRC and SRC cannot
achieve desirable performance especially when the dictionary
is not overcomplete enough, which is common in practical
FR system. Yang et al. [6] gave an insight into SRC and
provided some theoretical supports for its effectiveness. They
asserted that it is l
1
regularizer rather than l
0
(which counts
the number of nonzero entries in a vector) that renders SRC
resultful. Zhang et al. [7] analyzed the core theory of SRC
and argued that the collaborative mechanism plays a more
essential role than the l
1
-norm based sparsity constraint. They
proposed a collaborative representation classifier (CRC) based
on l
2
-norm constraint. By using of the structural information
of errors, Yang et al. [8] further proposed nuclear norm based
matrix regression (NMR) classification framework under l
2
-
norm regularization for better FR performance in the presence
of occlusion and illumination variations. Zhong et al. believed
that there should be a certain balance between SRC and CRC.
They introduced l
1/2
-norm regularization for the practical FR
which claimed to embrace both advantages of SRC and CRC
for better performance [9]. The label of the dictionary atoms
is not utilized in the aforementioned algorithms, hence their
regression is based solely on the structure of the individual
samples. Nie et al. introduced the l
2,1
-norm regularity term
to incorporate the class labels. Their method, named as group
sparse classifier (GSC), explores the sparse structure in the
group form with more discriminative information [10].
It is worth mentioning that, these classifiers and their
variants, however, still have not overcome the two elementary
constraints of regression type algorithms. One is the carefully
navigated importance of different samples and the other is
the removal of some invalid features. A violation of these
two conditions results in poor performance of the regression-
based classification [11], [12]. The first constrain makes all
the training samples equally contribute to discriminant, which
is unrealistic. The second constrain renders regression based
approaches perform poorly for the heavy corrupted query
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