# A Novel Fuzzy Kernel Extreme Learning Machine Algorithm in Classification Problems
###### Abstract  
Today, numerous methods have been developed to address various problems, each with its own advantages and limitations. To overcome these limitations, hybrid structures that integrate multiple techniques have emerged as effective computational methods, offering superior performance and efficiency compared to single-method solutions. In this paper, we introduce a basic method that combines the strengths of fuzzy logic, wavelet theory, and kernel-based extreme learning machines to efficiently classify facial expressions. We call this method the Fuzzy Wavelet Mexican Hat Kernel Extreme Learning Machine. To evaluate the classification performance of this mathematically defined hybrid method, we apply it to both an original dataset and the JAFFE dataset. The method is enhanced with various feature extraction methods. On the JAFFE dataset, the algorithm achieved an average classification accuracy of 94.55% when supported with local binary patterns and 94.27% with a histogram of oriented gradients. Moreover, these results outperform those of previous studies conducted on the same dataset. On the original dataset, the proposed method was compared with an extreme learning machine and wavelet neural network, and it was found that the method has remarkable efficiency compared to the other two methods. hybrid algorithms; facial expressions; classification; wavelet kernel; extreme learning machine  
with the advancing technological environment, soft methodologies including neural networks, fuzzy structure (logic), and wavelet structure have been applied to categorize facial expressions [3; 4; 5]. For example, [PERSON] et al. proposed a robust Gabor wavelet-based approach for facial gesture recognition and face identification that can reduce dimensions and improve discriminative capabilities as well as perform linear discriminant analysis. In their experiments, the proposed Gabor wavelet metric achieved a maximum 93% correct recognition rate on the ORL dataset without any preprocessing steps [6]. [PERSON] and [PERSON] showed that Kernel ELM, an extreme learning machine based on least square solutions, can be implemented using kernels for face recognition problems. The performances of kernel ELM were compared with traditional least squares support vector machines on a face recognition dataset [7]. [PERSON] and [PERSON] classified facial expression images into seven classes using BPNNs as classifiers. They applied three wavelet transforms (Haar, Daubechies, and Coiflet) for feature extraction and tested their method on the JAFFE database with promising results [8]. [PERSON] and [PERSON] presented an ELM-based facial expression recognition (FER) model. In their experiments, the face image is first captured and then some salient facial features such as the eyes, mouth, and nose are detected. The feature segments are extracted to form feature vectors through morphological image processing and edge detection techniques. Using ELM, facial expressions are classified into six basic categories on the JAFFE facial expression database [9]. [PERSON] and [PERSON] used Log Gabor wavelet filters for feature extraction in their study. This is because the wavelet structure is \"sensitive to changes in light and variations in pose\". In the classification stage, SVM was run on the JAFFE database [10]. [PERSON] et al. conducted extensive experiments on two reference datasets, JAFFE and Cohn-Kanade Extended (CK+). Their proposed methodology integrates meta-heuristic optimization algorithms (Whale) and a relatively new decomposition algorithm, Variational Mode Decomposition with KELM. The methodology was used as a classifier for the FER system [11]. [PERSON] and [PERSON] proposed an optimized KELM algorithm with ANFIS for an efficient FR system. In the experiment, the success of the hybrid technique was compared with the performance of existing methods in terms of various parameters (precision, sensitivity, etc.) and it was shown that the proposed FR system produced more efficient results [12].