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Discrete Firefly Algorithm Based Feature Selection Scheme for Improved Face Recognition.

1 Introduction

In the field of pattern recognition, face recognition (FR) has attracted interest from researchers due to its numerous applications such as law enforcement and commerce, public security, credit card verification access control, criminal identification, human-computer intelligent interaction, and information security and digital libraries (Bakshi et al., 2014). FR is a process of identifying a person's identity by matching input face biometrics as against a predefined face in a database (Zhou et al., 2014).

In day-to-day social activities and interactions, the face appears to be an important factor for easy identification (Shivdas, 2014). Face recognition has advantages over the traditional methods of identification, which involves the use of passwords and personal identification numbers that provide accuracy and its case sensitiveness (Angle et al., 2005; Kaur & Singh, 2015). It also offers non-contact process, captures or is videoed easily, provides reliable face matching, and offers a wide range of applications (Bakshi & Singhal, 2014).

The face acts as a key factor of consideration in the public domain, playing a foremost function in conveying uniqueness and emotion (Maini & Aggarwal, 2009). Basically, the face recognition system works in three stages which are: preprocessing (detection), feature extraction and classification (extraction) (Fernandes & Bala, 2017), and the choice of approach to each of these stages i.e. feature extraction (FE), feature selection (FS) and classification, is important to obtain better recognition accuracy (Bakshi et al., 2014).

In face detection, the aim is to locate an object contained inside an image as a specific face image that its shape looks like the shape of the face (Saleh, 2009). Face detection can be regarded as a process of automatically detecting a face from a complex background to which the face recognition algorithm can be applied. Several researchers used preprocessing (detection) at this stage (Agarwal & Bhanot, 2015).

In FE, high level information about individual patterns like the eyes, lips, eye brows, nose, which helps in facilitating recognition are extracted (Hemalatha & Govindan, 2015). The selection of the feature extraction technique is possibly the single most pertinent factor that aids in achieving optimal recognition performance (Saleh, 2009). Approaches used for FE include discrete cosine transform (DCT) (Hemalatha & Govindan, 2015; Jadon et al., 2015), Gabor wavelet filter (Keche et al., 2014; Ruan et al., 2010), principal component analysis (PCA) (Bakshi & Singhal, 2014; Satone & Kharate, 2014; Sawalha & Doush, 2012), local binary pattern (LBP) (Babatunde et al., 2015), and discrete wavelet transform (DWT) (Kallianpur et al., 2016; Manikantan et al., 2012).

In the classification (recognition) stage, face samples are compared or matched with the existing known faces in the database (Jagroop & Josan, 2013). Some methods reported at this stage are: support vector machine (SVM) (Satone & Kharate, 2014; Xu & Lee, 2014), Hidden Markov Model (HMM) (Jameel, 2015), nearest neighbor classifier (NNC) (Agarwal & Bhanot, 2015), back propagation neural network (BPNN) (Shivdas, 2014), and self-organizing map (SOM) (Bakshi & Singhal, 2014).

The process of the FS involves the determination of a feature subset which is then suitable to represent the specific feature set (Manikantan et al., 2012). FS problem is an interesting area, this is due to its combinatorial nature. FS phase of the FR process attempts to obtain the important discriminative features between the faces of two or more individuals in order to produce a high accuracy in the databases capturing differences in pose, occlusion or expression and illumination (Agarwal & Bhanot, 2015). Many amongst these features are not important features, and as such, it causes the face data to be over fitted, which eventually lowers the systems performance (Agarwal & Bhanot, 2015). Some of the artificial intelligence (AI) optimization technique used in feature selection include: particle swarm optimization (PSO) (Cervante et al., 2012; Hemalatha & Govindan, 2015; Ramadan & Abdel-Kader, 2009; Xue et al., 2014a; Xue et al., 2014b), firefly algorithm (FA) (Agarwal & Bhanot, 2015; Mistry et al., 2017b), genetic algorithm (GA) (Boubenna & Lee, 2016; Mistry et al., 2017a), ant colony optimization (ACO) algorithm by (Babatunde et al., 2015; Babatunde et al., 2017), artificial bee colony (ABC) optimization algorithm by (Kallianpur et al., 2016; Khan & Gupta, 2016), cuckoo search algorithm (CSA) by (Tiwari, 2012) and harmony search algorithms (HSA) (Sawalha & Doush, 2012).

However, all these algorithms are continuous and requires a continuous problem, thus the face recognition which is discrete requires to be converted to continuous, or the algorithm is converted to discrete which is time consuming. A discrete firefly (DFA) algorithm for feature selection is proposed to address this challenge, in order to improve recognition accuracy. The proposed DFA will be tested on the Olivetti Research Labs (ORL) and Yale facial images databases.

The outline of the paper is organized in sections. Section 2 discusses the FA algorithm and section 3 presents the discrete DFA for face recognition. Section 4 elaborates on the face recognition algorithm, and section 5 displays and discusses the simulation results of the DFA for face recognition, while lastly section 6 gives the conclusion.

2 Firefly Algorithm (FA)

Firefly algorithm (FA) is a meta-heuristic algorithm inspired by the flashing behavior of the natural fireflies. The firefly moves randomly in the search space to obtain the best position, so as to acquire the maximum brightness (Yang, 2009). The firefly moves towards the direction of a brighter firefly due to the attractiveness of the later firefly in the eyes of the former firefly. However, the attractiveness of a firefly depends on its own light, and on its distance from the firefly which is looking at it (Yang, 2009). The following three idealized rules are important to be highlighted for proper understanding of the FA (Osaba et al., 2017):

a. In a swarm, all the fireflies are unisex, and one firefly can be attracted to any other firefly regardless of their sex.

b. The brightness is proportional to the attractiveness, which implies that, for any two fireflies, the brighter firefly will attract the less bright firefly. The attractiveness also decreases as the distance between the firefies increases. However, if one firefly in the swarm is the brightest one, it will move randomly.

c. The brightness of a firefly is affected by the objective function of the problem. However, for a maximization problem, the brightness can simply be proportional to the objective function value (Lobato & Steffen, 2013). On the other hand, for a minimization problem, it can simply be the reciprocal of the objective function value (Lobato & Steffen, 2013).

The firefly's attractiveness at a distance 'r'is given by (Yang, 2009):

[mathematical expression not reproducible] (1)

[[beta].sub.o] represents the attractiveness at distance r = 0, and [gamma] (gamma) is the light absorption coefficient. The distance between two firefly i and firefly j at [x.sub.i] is derived using the Cartesian distance (Yang, 2009):

[mathematical expression not reproducible] (2)

[X.sub.i,k] represents the [k.sup.th] component of spatial coordinate [X.sub.i] of the [i.sup.th] firefly, and [X.sub.j,k] represents the [k.sup.th] component of spatial coordinate [X.sub.j] of the [j.sup.th] firefly.

The firefly's brightness is given by its fitness value. The firefly moves randomly in the search space and keeps acquiring new positions. If the new position is [X.sub.i] in the 'd' dimensional space, which is derived by a firefly [F.sub.i], then (Yang, 2009):

[mathematical expression not reproducible] (3)

The first term in equation (3) is the firefly's position reached so far, while the distance moved by [F.sub.i] is the second term, which is the less bright firefly, towards [F.sub.j], which is the brighter firefly. However, the random movement of a firefly is the third term. Also, the parameter [alpha] is the randomization parameter, while [[epsilon].sub.i] is a random value of vectors that are drawn from a uniform distribution or Gaussian distribution, which is randomly selected within the interval of [0 1] (Osaba et al., 2017). The flowchart of the FA is given in Figure 1.

3 Discrete Firefly Algorithm (DFA)

The classical algorithm of the FA was developed originally for solving continuous optimization problems, which requires a conversion to solve a discrete problem. For this reason, the classical FA cannot be applied directly to solve the proposed feature selection problem. Therefore, the discretization of the continuous FA is needed to address this problem (Karthikeyan et al., 2015). In the proposed DFA, each firefly in the swarm represents a possible and feasible solution for feature selection. All the fireflies are initialized randomly. Also, the concept of light absorption is also represented in this proposed DFA. In this case, [gamma] = 0.95, and this parameter is in a manner that was written in equation (3). The Hamming distance represents the distance between two fireflies (Osaba et al., 2016).

Lastly, movement of each firefly i is attracted to another brighter firefly j which is computed as (Osaba et al., 2017):

n = Random (2,[r.sub.ij][[gamma].sup.g]) (4)

[x.sub.i] = InsertionFunction ([x.sub.i], n) (5)

Where [r.sub.ij] represents the Hamming Distance between each firefly i and firefly j, and g also represents the iteration number. The length of the movement of a firefly is a random number, which is between 2 and [r.sub.ij]x[[gamma].sup.g], and the movement function is [x.sub.t].

However, for the movement function, the Insertion function was used, which is a function that selects and extracts feature subset randomly: n from feature set. This function considers the capacity constraint, in order to avoid infeasible solutions (Osaba et al., 2017).

In DFA variant of the work of Osaba et al. (2017), the fireflies do not have directions to move. Instead, the fireflies employs their movement using evolutionary strategies. As such, the movement of each firefly is done using n times the Insertion Function, which generate n potential successors. This formed the best firefly after these n movements, while a new firefly is generated (Osaba et al., 2017). The DFA flowchart is depicted in Figure 2.

4 Face Recognition Algorithm

In implementing the face recognition system, the steps presented in this section were followed. The first stage was achieved by training the images for detection and extraction which was done using discrete cosine transform (DCT) and Haar wavelet based discrete wavelet transform (DWT), the second stage was achieved also using discrete firefly algorithm (DFA) for feature selection, and finally the last stage involves using nearest neighbor classifier (NNC) for the classification of the images.

4.1 Discrete Cosine Transform (DCT)

This technique converts a spatial domain waveform into its constituent components represented by a set of coefficients (El Aroussi et al., 2008). However, it expresses a sequence of data points in terms of a sum of cosine functions oscillating at different frequencies (Jagroop & Josan, 2013). DCT has good performance in compaction efficiency, computationally efficient due to its relation to discrete Fourier transform. Its energy is concentrated on low frequencies for natural images due to the fact that natural images mostly possess low frequency features (El Aroussi et al., 2008). DCT is used in feature extraction for face images to reduce dimensionality and data compression (Jagroop & Josan, 2013). However, DCT is used in both holistic and feature appearance-based approach (El Aroussi et al., 2008). Amongst some common variants of DCT are: type-II DCT, and its inverse, and type-III DCT (IDCT). The feature extraction of DCT usually are of two broad stages: the first stage is applied on the entire image to obtain the coefficient, and the second stage uses some of these features for construction of feature vectors (Dabbaghchian et al., 2010).

DCT coefficients for an M X N image which represents a matrix that is 2D is given as (Dabbaghchian et al., 2010):

[mathematical expression not reproducible] (6)

Where:

[mathematical expression not reproducible] (7)

F (x, y) is the image intensity function, and F (U, V) is the DCT coefficient of a 2D matrix. Image size of M X N matrix for large values of discriminant coefficients can be estimated as (Dabbaghchian et al., 2010):

[mathematical expression not reproducible] (8)

4.2 Discrete Wavelet Transform (DWT)

Wavelet Transform is a popular tool in computer vision and image processing, for its ability to capture localized time-frequency information of image extraction (Xu & Lee, 2014). Wavelet used in discrete transform comes from the fact that they integrate to zero, wave up and down across the axis.

This property ensures that the data is not over represented. Wavelets are signals which are local in time and scale, and generally have an irregular shape (Dhoriya & Shah, 2014). DWT converts the images starting from the spatial domain to frequency domain where the images are divided by vertical and horizontal lines which could be divided into four parts to represent the first-order of DWT (Kaur & Kaur, 2017). The captured images of the face are signals that are represented in space and time, and can be approximated using the orthogonal basis functions. Wavelets are used for the multi-resolution analysis of the images of the face, in which they provide a means for localization of signals in both frequency and time (Dhoriya & Shah, 2014). Filters in DWT decomposition are designed in such a way that the successive layers of the pyramid include only details not considered by the proceeding level (Kaur & Singh, 2015). The decomposition of the data into different frequency ranges allows the isolation of the components of the frequency that are introduced by intrinsic deformations due to expression variations into certain sub-bands, and considers only sub-bands with most relevant information to better the data (Xu & Lee, 2014). DCT is often used in signal processing to represent a signal, the two dimensional DWT (2D-DWT) of an image is given as (Xu & Lee, 2014):

[mathematical expression not reproducible] (9)

Where i and, represents the binary scaling power, while k and h are constants of the filters.

4.3 Nearest Neighbor Classifier (NNC)

An essential classifier for the face recognition is the nearest neighbor classifier (NNC), which is one of the simplest classifiers that is used by researchers in the recent years to achieve a better classification rate. The aim of NNC is the determination of how close the samples are to the test samples (Kaur, 2012). An image in the test is recognized by assigning to it the label of the closest point in the learning set, in which the distance is measured between the image space (Zhu et al., 2015). The closeness between the data points in the kernel nearest neighbor (KNN) is chosen by the Euclidean distance. Between the pixels in a dataset, a distance is assigned. Euclidean distance is the distance between two pixels. The Euclidean distance is given as (Zhu et al., 2015):

[mathematical expression not reproducible] (10)

This Euclidean distance is by default in a KNN classifier. But the distance between the two features can be measured based on the one of the distance cosine and correlation (Kaur, 2012). KNN has a lesser execution time and better accuracy compared to other commonly used methods like hidden Markov model, and kernel method suite. It is best for classifying persons based on their images. The NNC does not require learning (since it is memory-based), it can be used even with few examples, it works very well in low dimensions for complex surfaces. However, it is slow in classification and, suffers from the curse of dimensionality (Zhu et al., 2015).

The block diagram of the proposed approach is shown in Figure 3, while Figure 4 shows the flowchart of the face recognition system.

5 Results and Discussions

The performance of the discrete firefly (DFA) algorithm was implemented using benchmark face database of Olivetti Research Labs (ORL) now known as AT&T and Yale face database. ORL face database consists of frontal images of 40 persons, which captures variations in illumination, accessories and pose like spectacles. The image of each person contains 10 samples each that were taken against a dark homogeneous background. Facial expressions with open or closed eyes, spectacles, smiling or not smiling and different environmental variations were captured in the database. The face images size is 92x112 pixels with 256 (8-bit) grey levels per pixel.

It consists of five samples for testing and five samples for training from each person. Figure 5 shows some images of the ORL face database.

The face database of Yale consists of 15 persons, and 11 samples of 165 images. The variations in expression like sadness, surprise, happy, normal, wink, sleepy and illumination like right, left and center are captured in the images. The face image size is 92x112 pixels.

It consist of five samples for testing and six samples for training from each person. This is shown in Figure 6.

The experiment was performed in MATLAB 2017a simulation environment on a 64-bit OS system, intel [R] core [TM] 15-3470 CPU@ 3.20GHZ with RAM 8.00GB. The DCT extracts low frequency while the DWT extracts the high frequency features for the feature extraction. The DCT transforms the face images of features from a 10x10 square windows that are from the upper most left corner. Next, all the coefficient of the third level DWT approximation coefficients of Haar wavelets are used in forming the initial feature vector. However, the size of the third level DWT coefficient matrix is 12x14 (i.e. 168), while the feature vector has a total size of 268. The population size of the firefly used in implementing the DFA is 20, and also the maximum number of iterations is 20.

The DFA algorithm, when implemented on ORL face database, achieved an average recognition accuracy of 97.75%, with a recognition time of 42.27 seconds for fifty runs, and the recognition time/image was 0.21 sec/image. Also, when the DFA algorithm was implemented on Yale face database, it achieved an average recognition accuracy of 89.30% with a recognition time of 40.33 seconds also for fifty runs, and the recognition time/image was 0.54 sec/image.

The proposed DFA algorithm was compared with other meta-heuristic algorithms done by other researchers like Firefly Algorithm (FA), Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Binary Particle Swarm Optimization (BPSO) Algorithm. The summary of the comparison of the DFA used for feature selection in face recognition with respect to the other algorithms using ORL Face Database is shown in Table 1.

Table 1, shows that the DFA algorithm has a better recognition accuracy than the other earlier works that was done on FR. This is due to the fact that some of the optimization techniques used in feature selection of the face recognition are continuous and requires a discrete process, while the face recognition itself is a discrete problem, and the DFA is a discrete algorithm: so employing a discrete algorithm for a discrete problem will provide a higher recognition accuracy.

6 Conclusion

This paper presents a discrete firefly algorithm (DFA) based feature selection scheme for face recognition system. Feature selection phase of the face recognition process attempts to obtain the most discriminative features between two or more individuals' faces to produce the best accuracy in the databases capturing variations in expression or occlusion, illumination and pose. Some of the optimization techniques used for the feature selection are continuous and requires a discrete process. DFA was employed for the feature selection. The DFA was implemented using benchmark face database of Olivetti Research Labs (ORL), now known as AT&T and Yale face database. The DFA gave an average recognition accuracy of 97.75%, with a recognition time of 42.27 seconds on the ORL face database, while the algorithm gave an average recognition accuracy of 89.30% with a recognition time of 40.33 seconds on Yale face database. Future research work should consider employing different discrete algorithms like discrete ant colony optimization (DACO), and discrete bat algorithm (DBA).

Acknowledgement

This research work is supported by the Control-and-Computer Research Group of the Department of Computer Engineering, Faculty of Engineering, Ahmadu Bello University, Zaria, Kaduna State Nigeria. Also, the authors will like to thank the anonymous reviewer and the chief Editor, Dr. Abel Usoro, for his insightful comments and suggestions, which have been greatly beneficial for improving the quality of this work.

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Shittu S. Danraka (1) Sani M. Yahaya (2), Aliyu D. Usman (3), Abubakar Umar (1*) and Ahmed M. Abubakar (1)

(1) Department of Computer Engineering, Ahmadu Bello University, Zaria, Kaduna-State Nigeria.

(2) Federal Polytechnic, Bida, Niger-State, Nigeria.

(3) Department of Communications Engineering, Ahmadu Bello University, Zaria, Kaduna-State Nigeria. Email: ssdanraka@gmail.com, sanimanyahaya@gmail.com, aliyuusman@gmail.com, abubakaru061010@gmail.com (*), muktyx5@yahoo.com

(*) Corresponding Author
Table 1: Comparison of DFA with other Algorithms Using ORL Face
Database

Authors         Year  Approach  Classifier  Recognition  Number of
                                Used        Accuracy     Training
                                                         Images Used

Liu and         2008  GA        K-NN        90.50%       5
Wang (2008)
(Cheng et al.,  2011  BPSO      Nearest     93.25%       5
                                Neighbor
2011)
Darestani et    2013  PSO       MLP         90.00%       5
al. (2013)
(Agarwal &      2015  FA        Nearest
Bhanot,                         Neighbor    94.38%       5
2015)
Proposed        2018  DFA       Nearest
DFA                             Neighbor    97.75%       5
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Author:Danraka, Shittu S.; Yahaya, Sani M.; Usman, Aliyu D.; Umar, Abubakar; Abubakar, Ahmed M.
Publication:Computing and Information Systems
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Date:Mar 1, 2019
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