ORIGINAL ARTICLE
Parity symmetrical collaborative representation-based
classification for face recognition
Xiaoning Song
1
•
Xibei Yang
2
•
Changbin Shao
2
•
Jingyu Yang
3
Received: 28 July 2015 / Accepted: 7 March 2016 / Published online: 17 March 2016
Springer-Verlag Berlin Heidelberg 2016
Abstract Although the subspace-based feature extraction
algorithms provided a feasible strategy to deal with the
classification of high-dimensional data, most of the existing
algorithms are locality-oriented and suffer from many
difficulties such as uncertain information associated with
dataset and small sample size problem. In this paper, we
propose a novel collaborative representation-based classi-
fication method using parity symmetry strategy for face
recognition. More specifically, we firstly synthesize a set of
parity symmetrical images by means of odd–even decom-
position theorem, aiming to augment the training set.
Secondly, each query sample is represented as a linear
combination of the training samples from the extended
training set, we then exploit the optimal representation of
each reconstructed image with relevant contribution from
each class. The final goal of the proposed method is to
generate the best parity symmetrical representation of the
query sample to perform robust face classification.
Experimental result s conducted on ORL, FERET, AR, PIE
and LFW face databases demonstrate the effectiveness of
the proposed method.
Keywords CRC Parity symmetry Major relevant
contribution Image recognition
1 Introduction
Recently, many researchers have been concerned about the
collaborative representation-based pattern classification
problem due to the great success of representation-based
learning methods [1–5] in image analysis, reconstruction
and recognition. Based on sparse representation theory,
Wright et al. [6, 7] firstly proposed a very interesting
approach, sparse representation-based classification (SRC),
for face recognition. The basic idea of SRC is to code the
query sample over a dictionary with sparsity constraint, by
which the solution of l
1
-norm minimization with sufficient
sparsity can be equivalent to the solution obtained by l
0
-
norm minimization. Here, ‘sparsity’ means that the repre-
sentation coefficients of most training samples are equal or
close to zero. Hence it is believed that the sparsity con-
straint can make the coding vector more discriminative so
as to achieve the high classification accuracy. Inspired by
SRC, Zhang et al. [8] discussed a collaborative represen-
tation-based classification (CRC) method and presented a
more general model, aiming to represent a test sample
using an untraditional dictionary. The final recognition is
performed by evaluating the collaborative representation
capability of each class and by assigning the query sample
to the class that has maximum representation capability. In
fact, CRC implies that the coefficients of some training
samples are close to zero and the representation coeffi-
cients can be measured by the l
2
-norm. Recently, some
very impressive surveys [9, 10] reviewed extensive sparse
representation algorithms and presented the relationships
among the different norms based sparse representation
& Xiaoning Song
xnsong@hotmail.com; xnsong@aliyun.com
1
School of Internet of Things Engineering, Jiangnan
University, Wuxi 214122, China
2
School of Computer Science and Engineering, Jiangsu
University of Science and Technology, Zhenjiang 212003,
China
3
School of Computer Science and Engineering, Nanjing
University of Science and Technology, Nanjing 210094,
China
123
Int. J. Mach. Learn. & Cyber. (2017) 8:1485–1492
DOI 10.1007/s13042-016-0520-4