Objective

2

Traditional sparse representation classification methods have drawn extensive attention due to the improved sparse classification capacity by means of high-dimensional data. However

they ignore the information redundancy between the gallery and query sets

thereby leading to the uncertainty of final recognized results. To address this issue

we propose a novel method by jointly using a convolutional neural network (CNN) and a PCA(principal component analysis)-constrained optimization model to perform sparse representation-based classification (EPCNN-SRC).

Method

2

In this study

we present a new sparse learning strategy based on CNN and PCA-constrained optimization model to perform sparse classification. The two critical contributions of this work are as follows. First

we utilize LDA (linear discriminant analysis) to enhance further the discriminative capacity of the collaborative representation classification. Second

we obtain robust face features by using a deep CNN. Specifically

for designing a classification method

we reconstruct PCA coefficients of training samples

which are achieved via PCA-constrained optimization. The objective of the proposed classification method is to use PCA plus LDA hybrid constrained model to enhance the discriminatory capacity of SRC. In the first phase

the proposed method seeks to achieve a compressive linear representation of the test samples. Our design achieves an accurate reconstruction of the test sample using sample space and principle coefficient space. The second phase further improves the discriminative capability of the PCA coefficient in representing a test sample

thereby obtaining a competitive optimization model for face classification. Assuming that a given dataset with multiple images per subject exists

the samples in each subject are stacked as vectors. Hence

an interclass variant dictionary can be constructed by subtracting the natural image from other images of the same class for training data augmentation. Many different approaches have been proposed by researchers to construct a variation dictionary. However

the idea of setting a variation dictionary can be the same

that is

to augment the training set. The constructed interclass dictionary contains all types of important difference information

such as illumination

expression

and other differences that the error cannot represent. To improve the optimization efficiency

we project the training samples into the PCA space

in which a new sparse representation model with PCA-constrained optimization is designed. The formula is described in this study. The strength of the proposed strategies lies in successfully constructing some optimization solutions using quadratic optimization in downsized coefficient subspace

thereby enhancing the collaborative and discriminative capacity of the dictionary to reconstruct the input images. Most existing sparse or collaborative representation methods focus on the training data augmentation for effective optimization to alleviate the adverse effect of the small sample size problem. However

the original dictionary is commonly built on a high-dimensional subspace. A typical example is found in some famous collaborative representation-based methods

such as ESRC(extended sparse representation-based classifier). The abundant hybrid training atoms with high dimensionality may lead to time-consuming and uncertainty in the dataset. In our method

original and within-class variations of one subject can be approximated by a collaborative linear combination of the other subjects

thereby integrating the dimensionality reduction of the training samples and the hybrid optimization process. With the PCA-constrained model

the ESRC decomposes the original face structure of the training set into the orthogonal components known as eigenfaces

and the transformed axes can be established as a set of biases

which represent the variations among the different subjects. Thus

our method can remarkably reduce the computational complexity. Meanwhile

CNNs have been successfully used in a wide range of computer vision and pattern recognition applications and become the mainstream in face biometrics. A CNN trained on a large number of face images can extract robust textural features for face recognition across a variety of appearance variations

such as pose

expression

illumination

and occlusion. To further improve the accuracy of the proposed system

we apply state-of-the-art deep CNN features to our model to improve the accuracy. Here

the proposed classification method is based on CNN features

which are different from widely used nearest neighbor classifiers with cosine and Euclidean distances. In the data processing phase

we use the pretrained VGG16 model for feature extraction. The extracted features from the original input face image can obtain better performance than the traditional sparse representation method

which uses the raw pixel intensities for classification. Therefore

the robust sample features in the process of classification perform a crucial role.

Result

2

The designed method has achieved better performance than the traditional sparse representation methods. We repeat each experiment 20 times in every dataset and compute the average value as the final recognition rate. We design an experiment in four different face datasets to evaluate the robustness of the proposed method. Each face dataset contains different styles and numbers in express and pose change. Results are compared with some traditional related classification methods

such as ESRC

NN_CNN(nearest neighbor convolutional neural networks)

CIRLRC (conventional and inverse representation-based linear regression classification)

TPTSR(two-phase test sample sparse representation)

SRICE (sparse representation using iterative class elimination)

SRC(sparse representation-based classifier)

CRC(collaborative representation based classification)

and LRC(linear representation classification). All the methods are operated under the same experimental condition. To confirm the capability of the method to alleviate the adverse effect of the small sample size problem

some experiments are performed in a single sample. The results obtained from the AR

FERET

FRGC

and LFW datasets show that when each subject has only one sample

the proposed EPCNN-SRC achieves 96.92%

96.15%

86.94%

and 42.44% recognition rates

respectively

which are higher than that of other traditional methods. This finding has fully provided the effectiveness of the proposed method. In addition

when the test environment contains complex changes

the algorithm still shows good recognition

particularly in terms of time complexity

which is considerably lower than that of the traditional representation classification algorithm

and achieves the expected results.

Conclusion

2

In this study

we propose EPCNN-SRC. Experiments in many datasets show that this algorithm

which applies iterative optimization strategy in feature space

not only effectively extracts the robust information features of the original samples but also combines norm and norm minimization to reduce the time cost of the representation classification algorithm. The key innovation of the proposed work is to accomplish face recognition using a novel dimensionality reduction optimization model

thereby resulting in robust SRC under appearance variations. The strength of the technique lies in successfully constructing a quadratic optimization in downsized coefficient solution subspace

thereby enhancing the discriminatory capacity of the dictionary to reconstruct input signals effectively. We believe that our promising results can encourage future works on synthesizing additional informative optimization structures and can improve this study for better SRC solutions.