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Multimed Tools Appl

DOI 10.1007/s11042-015-3042-2

Class specific centralized dictionary learning for face

recognition

Bao-Di Liu

· Liangke Gui

· Yuting Wang

Yu-Xiong Wang

· Bin Shen

· Xue Li

Yan-Jiang Wang

Received: 1 May 2015 / Revised: 15 August 2015 / Accepted: 22 October 2015

Abstract Sparse representation based classification (SRC) and collaborative representation

based classification (CRC) have demonstrated impressive performance for visual recogni-

tion. SRC and CRC assume that the training samples in each class contribute equally to

the dictionary and thus generate the dictionary that consists of the training samples in the

corresponding class. This may lead to high residual error and instability, to the detriment

 Bao-Di Liu

thu.liubaodi@gmail.com

Liangke Gui

liangkeg@cs.cmu.edu

Yuting Wang

utdyc@student.kit.edu

Yu-Xiong Wang

yuxiongw@cs.cmu.edu

Bin Shen

bshen@purdue.edu

Xue Li

lixue421@gmail.com

Yan-Jiang Wang

yjwang@upc.edu.cn

College of Information and Control Engineering, China University of Petroleum, Qingdao

266580, China

School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA

Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China

Department of Informatics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany

Multimed Tools Appl

of recognition performance. One solution is to use the class specific dictionary learning

(CSDL) algorithm, which has greatly improved the classification accuracy. However, the

CSDL algorithm fails to consider the constraints to sparse codes. In particular, it cannot

guarantee that the sparse codes in the same class will be concentrated based on the learned

dictionary for each class. Such concentration is actually beneficial to classification. To

address these limitations, in this paper, we propose a class specific centralized dictionary

learning (CSCDL) algorithm to simultaneously consider the desired characteristics for both

dictionary and sparse codes. The blockwise coordinate descent algorithm and Lagrange

multipliers are used to optimize the corresponding objective function. Extensive experimen-

tal results on face recognition benchmark datasets demonstrate the superior performance of

our CSCDL algorithm compared with conventional approaches.

Keywords Centralized dictionary learning · Face recognition · Class specific

1 Introduction

After decades of effort, the power of dictionary learning for sparse representation has

been gradually revealed in visual computation areas, such as image annotation [25], image

inpainting [30], image classification [14, 16], face recognition [32], object detection [28],

transfer learning [29], and image denoising [6], due to its impressive performance. Differ-

ent from traditional decomposition frameworks like principal component analysis (PCA),

non-negative matrix factorization [31], and low-rank factorization [27], sparse representa-

tion allows coding under over-complete bases (that is, the number of bases is greater than

the dimension of input data), and thus generates sparse codes capable of representing the

data more adaptively.

Face recognition, one of the successful applications of sparse representation, is a classi-

cal yet challenging research topic in computer vision and pattern recognition [38]. Effective

face recognition usually involves two stages: 1) feature extraction, 2) classifier construc-

tion and label prediction. For the first stage, Eigenfaces were proposed by performing

PCA [24]. Laplacianfaces were proposed to preserve local information [9]. Fisherfaces

were suggested to maximize the ratio of between-class scatter to within-class scatter [1].

Yan et al. [33] proposed a multi-subregion based correlation filter bank algorithm to extract

both the global-based and local-based face features. For the latter stage, a nearest neighbor

method was proposed to predict the label of a test image using its nearest neighbors in the

training samples [5]. Nearest subspace methods were proposed to assign the label of a test

image by comparing its reconstruction error for each category [10, 22].

Under the nearest subspace framework, a sparse representation based classification

(SRC) system was proposed and achieved impressive performance [32]. Given a test sam-

ple, the sparse representation technique represents it as a sparse linear combination of the

training samples. The predicted label is determined by the residual error from each class. To

analyze SRC, collaborative representation based classification (CRC) was proposed as an

alternative approach [36]. CRC represents a test sample as the linear combination of almost

all the training samples. An interesting observation in [36] is that it is the collaborative rep-

resentation rather than the sparse representation that makes the nearest subspace method

powerful for classification.

Despite their promise, both SRC and CRC algorithms directly use the training sam-

ples as the dictionary for each class. By contrast, a well learned dictionary, especially by

Multimed Tools Appl

enforcing some discriminative criteria, can reduce the residual error greatly and achieve

superior performance for classification tasks. Existing discriminative dictionary learning

approaches are mainly categorized into three types: shared dictionary learning, class specific

dictionary learning, and hybrid dictionary learning. In shared dictionary learning, each basis

is associated to all the training samples. Mairal et al. [18] proposed to learn a discrimina-

tive dictionary with a linear classifier of coding coefficients. Liu et al. [17] learned a Fisher

discriminative dictionary. Zhang and Li [37] proposed a joint dictionary learning algorithm

for face recognition. In class specific dictionary learning, each basis only corresponds to a

single class so that the class specific reconstruction error could be used for classification.

Yang et al. [35] learned a dictionary for each class with sparse coefficients and applied it

for face recognition. Sprechmann and Sapiro [21] also learned a dictionary for each class

with sparse representation and used it in signal clustering. Castrodad and Sapiro [3] learned

a set of action specific dictionaries with non-negative penalty on both dictionary atoms

and representation coefficients. Wang et al. [26] introduced mutual incoherence informa-

tion to promote class specific dictionary learning in action recognition. Yang et al. [34]

embedded the Fisher discriminative information into class specific dictionary learning. Self-

explanatory sparse representation based dictionary learning was suggested to enhance the

interpretation of the class specific based dictionary learning algorithm [13].

The shared dictionary learning approaches usually lead to a dictionary of small size and

the discriminative information (i.e., the label information corresponding to coding coeffi-

cients) is embedded into the dictionary learning framework. The class specific dictionary

learning approaches usually focus on the classifier construction aspect since each basis vec-

tor is fixed to a single class label. The combination of shared basis vectors and class specific

basis vectors is then learned in hybrid dictionary learning. Zhou et al. [39] learned a hybrid

dictionary with Fisher regularization on the coding coefficient. Gao et al. [7] learned a

shared dictionary to encode common visual patterns and learned a class specific dictionary

to encode subtle visual differences among different categories for fine-grained image rep-

resentation. Liu et al. [12] proposed a hierarchical dictionary learning method to produce a

shared dictionary and a cluster specific dictionary. In spite of the demonstrated performance

of hybrid dictionary learning, it is still a challenge to balance between the shared dictionary

and the class specific dictionary.

Compared with SRC, the conventional class specific dictionary learning approach [35]

enhances the discrimination to some extent by learning a dictionary for each class. However,

it is likely that the sparse codes obtained by the corresponding dictionary in one class and the

sparse codes in other classes are interdependent, leading to erroneous discrimination. Such

interdependence among classes could be potentially reduced by centralized sparse codes.

In this paper, motivated by the superior performance of class specific dictionary learning

and the benefit of centralized sparse codes, we propose class specific centralized dictionary

learning (CSCDL) for sparse representation based classification. Our key insight is to make

the sparse codes in the same class concentrated. The main contribution is three-fold:

•

A novel class specific centralized dictionary learning (CSCDL) approach is proposed,

which is capable of guaranteeing the sparse codes in the same class concentrated.

•

Blockwise coordinate descent and Lagrange multipliers are used to efficiently solve the

corresponding optimization problems.

•

Our proposed CSCDL algorithm achieves superior performance on several benchmark

datasets for face recognition tasks, which demonstrates its effectiveness.

The rest of the paper is organized as follows. Section 2 reviews conventional sparse

representation based classification and collaborative representation based classification

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