I Introduction
Emotion recognition is an important area of research to enable effective humancomputer interaction. Human emotions can be detected using speech signal, facial expressions, body language, and electroencephalography (EEG), etc. In this paper, we focus on facial expression recognition (FER), which is a widely being studied problem [1, 2]. FER has become a very interesting field of study and its applications are not limited to human mental state identification and operator fatigue detection, but also to other scenarios where computers (robots) play a social role such as an instructor, a helper, or even a companion. In such applications, it is essential that computers are able to recognize human emotions and behave according to their affective states. In healthcare, recognizing patients’ emotional instability can help in early diagnosis of psychological disorders [3]. Another application of FER is to monitor human stress level in daily humancomputer interaction.
Humans can easily recognize another human’s emotions using facial expressions but the same task is very challenging for machines. Generally, FER consists of three major steps as shown in the Figure 1
. The first step involves the detection of a human face from the whole image by using image processing techniques. In the second step, key features are extracted from the detected face. Finally, machine learning models are used to classify images based on the extracted features.
Features descriptors like histograms of oriented gradients (HOG) [4], Local Gabor features [5] and Weber Local Descriptor (WLD) [6] are widely used techniques for FER, whereas HOG has shown to be particularly effective in literature for the task of FER [7]
. The dimensionality of these features is usually high. Due to the complexity of multiview features, dimension reduction and more meaningful representation of this high dimensional data is a challenging task. Therefore, techniques like Principal Component Analysis (PCA) and Local Binary Pattern (LBP),
[8, 5], NonNegative Matrix Factorization (NMF), etc., are being used to overcome high dimensionality problem by representing the most relevant features in lowerdimensions.Machine learning techniques have revolutionized many fields of science including computer vision, pattern recognition, and speech processing through its powerful ability to learn nonlinear relationships over hidden layers, which makes it suitable for automatic features learning and modeling of nonlinear transformations. Deep neural networks (DNNs) can be used for feature extraction as well as for dimensionality reduction
[9, 7]. A large number of classification techniques has been used for FER. For example, Choi et al. [10] used artificial neural networks (ANNs) for classification of facial expressions. Authors in [8, 11]have used Support Vector Machines (SVMs) for FER. In
[12, 13], authors utilized Hidden Markov Model (HMM) for FER. HMMs are mostly used for framelevel features to handle sequential data. Besides these classifiers, Dynamic Bayesian Networks
[14][15]are also utilized for learning facial expressions. The recent success of deep learning also motivates its use for FER
[16, 17].In this paper, we use a novel approach based on stacked autoencoders for FER. We exploited autoencoders network for effective representation of high dimensional facial features in lower dimensions. Autoencoders represent an ANN configuration in which output units are linked to the input units through the hidden layers. A fewer number of hidden units allow them to represent input data into a low dimensional latent representation. While in stacked autoencoder, output of first layer is immediately given to second layer as an input. In other words, stacked autoencoders are built by stacking additional unsupervised feature learning hidden layers, and can be trained by using greedy methods for each additional layer. As a result, when the data is passed through the multiple hidden layers of stacked autoencoders, it encodes the input vector in a smaller representation more efficiently [18]. In our case, autoencoders network is more suitable as it not only reduces the dimension of data but can also detect most relevant features. In previous work, Hinton et al. [19] have shown that autoencoders networks can be used for effective dimension reduction and they can produce more effective representation than PCA.
For our experiments, we choose Extended CohnKanade (CK+) [20] dataset which is extensively used for automatic facial image analysis and emotion classification. The HOG features are computed from the selected area of facial expressions and their dimensions have been reduced by using stacked autoencoders on multiple levels and with multiple hidden layers to get the most optimal encoded features. SVM model in the onevsall scenario is used for classification on this reduced form of features. We have performed multiple experiments on the selection of optimal dimension (10500 features) of the feature vector. The feature vector with length 60, obtained after the introduction of four hidden layers in autoencoders network outperformed as compared to other dimensions. Most importantly, we also use PCA for dimension reduction in order to compare the baseline results with autoencoders. Our proposed method for FER using stacked autoencoders is also outperformed when results were compared with PCA and other recent approaches published in this domain. This demonstrates the effectiveness of stacked autoencoders for the selection of the most relevant features for FER task.
Ii Related Work
Facial expressions are visually observable nonverbal communication signals that occur in response to a person’s emotions and originate by the change in facial muscle. They are the key mechanism for conveying and understanding emotions. Ekman and Freisen [21] postulated six universal emotions (i.e., anger, fear, disgust, joy, surprise, and sadness) with distinct content and unique facial expression. Most of the studies in the area of emotion recognition usually focus on classifying these six emotions.
Much of the efforts have been made to classify facial expression with various facial feature by using machine learning algorithms. For example, Anderson et al. [22]
developed an FER system to recognize the six emotions. They use SVM and Multilayer Perceptrons and achieved a recognition accuracy of 81.82%. In
[6], Wang et al. combined HOG and WLD features to have missing information about the contour and shape. The proposed solution attained 95.86% recognition rate by using chisquare distance and the nearest neighbor method to classify the fused features. Lia et al. [23] used knearest neighbor to compare the performance of PCA and NMF on Taiwanese and Indian facial expression databases. They attained above 75% recognition rate by using both techniques.Recently, a comprehensive study has been made by Liu et al. [8], they also combined HOG with Local Binary Patterns (LBP) features. For dimension reduction of extracted features, PCA was used. After applying several classifiers on reduced features, he received 98.3% maximum recognition rate. Similarly, Xing et al. [24] used local Gabor features with Adaboost classifier for FER and achieved 95.1% accuracy with the 10time reduced dimensionality of traditional Gabor features.
Encouragingly, Jung et al. [25] used deep neural networks to extract temporal appearance as well as temporal geometric features from RAW data. They tested this technique on several datasets and obtained higher accuracy than stateoftheart techniques. Jang et al. [26] worked on color images and attained 85.74% recognition rate by using color channelwise recurrent learning using deep learning. Similarly, Talele et al. [27] used LBP features and ANN for classification and the maximum success rate was 95.48%.
Recently, the autoencoders models have been used more widely for features learning from data and classification problems. For example, Huang et al. [28] used sparse autoencoder networks for feature learning and classification. His technique was good to avoid human interaction but at the cost of computation complexity. Interestingly, Gupta et al. [29] developed a multivelocity autoencoder network by using the multivelocity layers for generating velocityfree deep motion features for facial expressions. The proposed technique attained the stateoftheart accuracy on various FER datasets. An interesting work has been done by Makhzan et al. [30]
to investigate the effectiveness of sparsity on MNIST data. They showed that sparse autoencoders are simple to train and achieve better classification results as compared to the denoising autoencoders and Restricted Boltzmann Machines (RBMs) as well as networks trained with dropout. Another study
[31] explored the effect of hidden layers in stacked autoencoders on MNIST data. The authors showed that stacked autoencoders with larger depth have better learning capability but require more training examples and time.Iii Proposed Method
Our proposed FER system consists of four steps (as illustrated in Figure 2). The first step is related to image processing, in which, we use the stateoftheart Viola Jones [32]face detection method for face detection and extraction. This extracted portion represents the most variance when expression changes. In the second step, HOG features are computed from the cropped image. In the third step, highdimensional HOD features are reduced to lower dimension using stacked autoencoders. Finally, in the fourth step, the SVM model is used on these lower dimension features to classify the facial expressions. Extended CohnKanade Dataset (CK+) is used in our experiment. Most importantly, we investigated the performance of encoded features of length 5 to 100 using different depth of stacked autoencoders.
Figure. 2 shows the flowchart of our overall experiment. The detail of each step is given below.
Iiia Image Processing
At the image processing stage, we first detect and extract the face region to eliminate redundant regions which can affect recognition rate. The used databases contain much redundant information in the images, and to eliminate the redundant information, the robust realtime detector developed by Viola and Jones [32] is employed. In this way, we obtained the face local region around mouth and eyes as these parts represent the most discriminating information when facial expression changes.
As shown in Figure. 3, we crop out the face region and resize the face image to 128128 to get the salient areas of facial expression.
IiiB Feature Extraction
Histogram of oriented gradients (HOG) is a feature descriptor which is widely used in computer vision and image processing [33]. The technique counts occurrences of gradient orientation in localized portions of an image. HOG is invariant to geometric and photometric transformations, except for object orientation. The images that are in the database have different expressions and different orientations of eyes, nose, and lip corners. HOG is used in our algorithm because it is a powerful descriptor to detect the variations (i.e., when facial expressions change). In our proposed approach, we applied HOG on cropped face images and extracted the feature vectors. The cropped image of size 128128 gives a feature vector of size 18100 using HOG. The feature vectors are concatenated to form feature matrix as shown in table I.
1x8100 (HOG Feature of image 1) 

1x8100 (HOG Feature of image 2) 
1x8100 (HOG Feature of image 3) 
1x8100 (HOG Feature of image 4) 
………… 
………… 
………… 
………… 
1x8100 (HOG Feature of image (N1)) 
1x8100 (HOG Feature of image N) 
IiiC Dimension Reduction
The main aim of this work is to show that how nonlinear machine learning technique can be effectively used to obtain the most relevant holistic representation of features in a lower dimension. As the extracted HOG features have a high dimension (N8100) as compared to the number of available images (327). The stateoftheart is to reduce the dimension of the features vector by using different dimension reduction techniques such as PCA, linear discriminant analysis (LDA) and NMF. For this purpose, we use autoencoder network on high dimensional feature descriptors extracted by using HOG. To compare the performance of these features, we also use PCA for dimension reduction of features. Both of these techniques are discussed below.
IiiC1 Autoencoders
An autoencoder is an unsupervised architecture that replicates the given input at its output. It takes an input feature vector
and learns a code dictionary by changing the raw input data from one representation to another. An autoencoder applies backpropagation by setting the target values to be equal to the inputs (i.e.,
) as shown in the Figure 4.For example, if autoencoders are inputted with correlated structural data, then the network will discover some of these correlations [34]. In an autoencoder, the lower dimension is represented by
(1) 
Where is associated weight vector with the input unit and hidden unit, is the bias associated with the hidden unit and is the activation of the hidden unit in the network. Similarly,
is the sigmoid function that is given by
(2) 
(3) 
and
(4) 
The stacked autoencoder can be described as follow
(5) 
Encouragingly, an autoencoder can also discover the interesting structure of data, even when the number of hidden units is large, by imposing sparsity constraint on the hidden units. Such architecture is called sparse autoencoder. The cost function of a sparse autoencoder is given by:
(6) 
Where
is an activation function,
and are weights and biases respectively. The first term in equation (IIIC1) tries to minimize the difference between the input and output. The second term is the weight decay that avoids overfitting, where is the parameter for weight decay, is the number of layers in autoencoder network, and denotes the number of units for the layer. Similarly, represents the weight value between the unit of layer and the unit of layer , and is the bias associated with unit in layer . The last term is a sparse penalty term, where controls the weight of this term, and is a sparsity parameter and is the KullbackLeibler () divergence that is given by(7) 
Typically, is set to be a small value close to . divergence is a standard function used for measuring the difference between two different distributions.
In this experiment, the extracted features using HOG is inputted to autoencoder network to encode them at the desired level of dimension by limiting the hidden units in hidden layers. The number of hidden layers is always experiential. Therefore, we also tried to explore the effect of an increase in the number of hidden layers for stacked autoencoder. This effect typically used for dimension reduction of input data. We have performed multiple experiments to validate our findings. To get a quality of encoded features from autoencoder, we use backpropagation for finetuning of network parameters. Mean square error (MSE) is used as a loss function with 400 epochs.
IiiC2 Principal Component Analysis
The research domain of pattern recognition and computer vision is dominated by the extensive use of PCA which is also referred as KarhunenLoeve expansion [35]. PCA is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. PCA is an effective method to reduce the feature dimension and has been extensively being applied in FER for dimension reduction of features [8, 5]. Therefore, we chose PCA to compare its performance with nonlinear dimension reduction by autoencoder. High dimension feature matrix (N8100) is reduced to the multiple numbers of dimension (i.e., 10 to 500) using PCA.
IiiD Support Vector Machine
SVMs are very powerful tool for binary as well as multiclass classification problems. Initially, SVMs was designed for binary classification that separates the binary class data (=2) with a maximized margin. However, for realworld problems, it is often required to discriminate between data for more than two (2) categories. Therefore, two representative ensemble schemes exist in SVMs, i.e., oneversusall and oneversusone to classify multiclass data. In this experiment, we use SVM in the onevsall scenario with a Gaussian kernel function. In onevsall scheme, SVM constructs separate binary classifiers to classify classes of data. The binary classifier is trained by using the data from class as the positive example and the remaining number of classes as negative examples. During testing, the class label is predicted by the binary classifier that gives maximum output value. For binary classification task with training data and corresponding labels , the decision function can be formulated as:
(8) 
Where denotes a separating hyperplane, is a weight vector normal to the separating hyperplane and denotes the bias or offset of the hyperplane. Following is the region between hyperplanes that is also called margin band.
(9) 
Finally, choosing the optimal values of and is formulated as a optimization problem, where equation 9 is maximized subject to the following constrain:
(10) 
Iv Experimental Results and Discussion
The performance of our proposed approach for FER has evaluated on publicly available CK+ database. This dataset contains 593 sequences of images from 123 subjects. Only 327 out of 593 sequences of images are given the labels for 7 human facial expressions. Out of 7 expressions, we used six expressions (i.e., angry, happy, disgust, sadness, surprise, and fear) similar to the methods adopted in [18, 36, 8]. Contempt has only 18 labeled images so it was not included in our experiment. Each expressional image sequence starts with a neutral expression and ends with a peak expression (i.e., anger). In our experiment, we use five peak images of each expression to incorporate the temporal information of an expression. Figure. 5 shows a sample sequence of images for the six emotions that we use for training. For training, we use 80% of data while testing was performed using remaining 20%. During testing, we only use one peak image of each expression.
Multiclass SVM in the onevsall scheme with Gaussian kernel has been used for classification of facial expressions using MATLAB. We have performed multiple experiments on a different length of features obtained by autoencoder and PCA as shown in table II. It can be noted that encoded features obtained by the stacked autoencoders mostly outperformed the baseline (PCA) performance. By using autoencoder for dimension reduction, we achieved the highest recognition rate of 99.60% with 60 dimensions while with PCA 96.44% success rate is obtained with 80 dimensions.
Number of Feature  PCA (Accuracy %)  Autoencoders (Accuracy %)  









































We also investigated the effect of adding more hidden layers in autoencoder network. We have performed multiple experiments by introducing more hidden layers with a different number of hidden units (i.e., 500, 400, 300 and 200) while the encoded features are from 5 to 100. Figure 6 shows the structure of five autoencoders used in our experiments.
Table III shows the results of experiments in which a different number of hidden layers are introduced. It can be noted that higher the number of hidden layers not necessarily increase the accuracy, as already indicated in [37, 38]. From these results, we can state that after a certain number of the hidden layer for each number of feature, the accuracy starts decreasing. For example, with 80 features, when hidden layers are introduced, recognition rate increases till the second layer but after that, it decreases. Similarly, we find the same trend for all number of features but at a different number of hidden layers.
Number of Feature  Hidden Layer 1  Hidden Layer 2  Hidden Layer 3  Hidden Layer 4  Hidden Layer 5  
















































Figure. 7 shows the trend of best recognition rate and the number of reduced dimensions with autoencoder and PCA. It can be seen from Figure. 7 that there is no regular relationship between accuracy and the number of dimensions, however, it remains almost same after the specific dimension, i.e., 200.
The accuracy of 99.60 with less (i.e., 60) number of features is not reported in the literature. We have also revived the latest papers in table IV, to compare our method with recently published papers in this domain. It can be seen from table IV, previously maximum achieved accuracy is 99.51% using a combination of features (i.e, HOG+LDA+PCA). Similarly, Liu et al. [8] achieved 98.3% recognition rate using local binary patterns (LBP) and HOG features together. They achieved this accuracy using a combination of features with 80 dimensions. While our proposed method has shown significantly better results while using a single type of features at lower dimensions.
Study  Year  Method  Accuracy (%)  

























Although our proposed approach has achieved a stateoftheart recognition rate but the time complexity of autoencoders is linearly dependent on the number of features and hidden layers. Greater the number of features or hidden layers, the more time that is required to train the model.
V Conclusion
The main contribution of this paper is to investigate the performance of deep autoencoders for lower dimensional feature representation. The experiment proves that nonlinear dimension reduction using autoencoders is more effective than linear dimension reduction techniques for FER. We used CK+ dataset in our experiments and compared our results using features obtained by autoencoder networks with stateoftheart PCA. Most importantly, we explored the effect of an increase in the number of hidden layers which enhanced the learning capability of the network to provide more robust and optimal features for facial expression recognition.
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