The convolutional neural network (CNN) has been widely used in image recognition field due to its good performance. This paper proposes a facial expression recognition method based on the CNN model. Regarding the complexity of the hierarchic structure of the CNN model, the activation function is its core, because the nonlinear ability of the activation function really makes the deep neural network have authentic artificial intelligence. Among common activation functions, the ReLu function is one of the best of them, but it also has some shortcomings. Since the derivative of the ReLu function is always zero when the input value is negative, it is likely to appear as the phenomenon of neuronal necrosis. In order to solve the above problem, the influence of the activation function in the CNN model is studied in this paper. According to the design principle of the activation function in CNN model, a new piecewise activation function is proposed. Five common activation functions (i.e., sigmoid, tanh, ReLu, leaky ReLus and softplus–ReLu, plus the new activation function) have been analysed and compared in facial expression recognition tasks based on the Keras framework. The Experimental results on two public facial expression databases (i.e., JAFFE and FER2013) show that the convolutional neural network based on the improved activation function has a better performance than most-of-the-art activation functions.

As an important part of emotion research, facial expression recognition is a necessary requirement in human–machine interface. Generally, a face expression recognition system includes face detection, feature extraction, and feature classification. Although great success has been made by the traditional machine learning methods, most of them have complex computational problems and lack the ability to extract comprehensive and abstract features. Deep learning-based methods can realize a higher recognition rate for facial expressions, but a large number of training samples and tuning parameters are needed, and the hardware requirement is very high. For the above problems, this paper proposes a method combining features that extracted by the convolutional neural network (CNN) with the C4.5 classifier to recognize facial expressions, which not only can address the incompleteness of handcrafted features but also can avoid the high hardware configuration in the deep learning model. Considering some problems of overfitting and weak generalization ability of the single classifier, random forest is applied in this paper. Meanwhile, this paper makes some improvements for C4.5 classifier and the traditional random forest in the process of experiments. A large number of experiments have proved the effectiveness and feasibility of the proposed method.

The decision tree algorithm is a core technology in data classification mining, and ID3 (Iterative Dichotomiser 3) algorithm is a famous one, which has achieved good results in the field of classification mining. Nevertheless, there exist some disadvantages of ID3 such as attributes biasing multi-values, high complexity, large scales, etc. In this paper, an improved ID3 algorithm is proposed that combines the simplified information entropy based on different weights with coordination degree in rough set theory. The traditional ID3 algorithm and the proposed one are fairly compared by using three common data samples as well as the decision tree classifiers. It is shown that the proposed algorithm has a better performance in the running time and tree structure, but not in accuracy than the ID3 algorithm, for the first two sample sets, which are small. For the third sample set that is large, the proposed algorithm improves the ID3 algorithm for all of the running time, tree structure and accuracy. The experimental results show that the proposed algorithm is effective and viable.

In recent years, with the development of artificial intelligence and human–computer interaction, more attention has been paid to the recognition and analysis of facial expressions. Despite much great success, there are a lot of unsatisfying problems, because facial expressions are subtle and complex. Hence, facial expression recognition is still a challenging problem. In most papers, the entire face image is often chosen as the input information. In our daily life, people can perceive other’s current emotions only by several facial components (such as eye, mouth and nose), and other areas of the face (such as hair, skin tone, ears, etc.) play a smaller role in determining one’s emotion. If the entire face image is used as the only input information, the system will produce some unnecessary information and miss some important information in the process of feature extraction. To solve the above problem, this paper proposes a method that combines multiple sub-regions and the entire face image by weighting, which can capture more important feature information that is conducive to improving the recognition accuracy. Our proposed method was evaluated based on four well-known publicly available facial expression databases: JAFFE, CK+, FER2013 and SFEW. The new method showed better performance than most state-of-the-art methods.

As an important part of emotion research, facial expression recognition is a necessary condition for intelligent interaction between human and machine, which has an important research significance and a potential commercial value. Convolutional neural network (CNN) is an effective method to recognize facial emotions, which can perform feature extraction and classification simultaneously, and can automatically discover multiple levels of representations in data. Due to the fact that there are millions of parameters involved in training the convolutional neural network model, and there is a large demand for marked samples, transfer learning is often used to fine-tune the pre-trained model for a small target sample set. However, there are often some content differences between data sets during deep transfer learning, which will affect the recognition ability of feature extraction. In order to improve the facial expression recognition ability in transfer learning, a hybrid transfer learning model based on an improved convolution restricted boltzmann machine (CRBM) model and a CNN model is proposed in this paper. This method is fused by two learning abilities of these two models. When the pre-trained CNN model is transferred to a small target set, the CRBM is used to replace the full connection layer in the CNN model, and the CRBM layer and the sofmax layer will be retrained on the target set. The added CRBM layer can not only fully connects all feature maps, but can also learn about the unique statistical characteristics about the target set, which eliminates the influence of content differences between data sets, and extracts higher-order statistical features of facial expression images from the target set. The proposed method is evaluated based on four publicly available facial expression databases: JAFFE, FER2013, SFEW and RAF-DB. The new method can achieve better performance than most state-of-the-art methods, and it can effectively prevent the negative influence of transfer learning features between different data sets.

The identification difficulties for a dual-rate Hammerstein system lie in two aspects. First, the identification model of the system contains the products of the parameters of the nonlinear block and the linear block, and a standard least squares method cannot be directly applied to the model; second, the traditional single-rate discrete-time Hammerstein model cannot be used as the identification model for the dual-rate sampled system. In order to solve these problems, by combining the polynomial transformation technique with the key variable separation technique, this paper converts the Hammerstein system into a dual-rate linear regression model about all parameters (linear-in-parameter model) and proposes a recursive least squares algorithm to estimate the parameters of the dual-rate system. The simulation results verify the effectiveness of the proposed algorithm.