# A Novel Fuzzy Kernel Extreme Learning Machine Algorithm in Classification Problems
###### Abstract
Undoubtedly, these methods have both strengths and disadvantages. Therefore, recent studies have proposed more efficient hybrid algorithms by combining their strengths and camouflaging their weaknesses. For example, [PERSON] and [PERSON] integrated neural networks with a fuzzy structure to solve complex problems with uncertain parameters more efficiently [13]. [PERSON], [PERSON], and [PERSON] created a new algorithm called Fuzzy Wavelet Neural Network, which aims to test the time frequency and multiresolution of a wavelet structure and its capacity to independently stop a set of responses [14]. In 'Extreme Learning Machine: RBF Network Case', [PERSON] and [PERSON] extended the LMM structure to the radial basis function (RBF) network case [15]. Later, [PERSON], [PERSON], and [PERSON] introduced a single hidden layer FF neural network, called the extreme learning machine (ELM), to overcome the problems of classical neural networks such as long computation time and becoming stuck at local optima [16]. [PERSON] and [PERSON] proposed the WNN structure integrating wavelet structure and neural networks to overcome the disadvantage that backpropagation approaches local minima when adopting a sigmoidal activation function [17; 18]. [PERSON] et al. integrated wavelet neural networks (RNNs) with an FF error backpropagation artificial neural network (FEBANN) and used the algorithm as a classifier [19]. [PERSON] and [PERSON] introduced the FWNN model by replacing the THEN structure of the Takagi-Sugeno-Kang fuzzy rule set with a wavelet function [20]. Finally, [PERSON], [PERSON], and [PERSON] combined a fuzzy wavelet structure with ELM methods to reduce network complexity and introduced the fuzzy wavelet extreme learning machine (FW-ELM) framework [21]. Considering all the above-mentioned issues, in this study we suggest a hybrid baseline algorithm based on fuzzy logic, wavelet structure, and kernel-based extreme learning machines (KELMs) for facial expression classification problems. The hybrid approach is composed of a fuzzy wavelet network and a KELM to form a simple network structure, improve performance accuracy, and mitigate the effect of parameters randomly assigned by the researcher, and the structure is named FWMHKELM and is presented in Figure 1.  
The main motivation of the paper is to present the construction of a hybrid baseline algorithm that provides robust results in solving problems related to facial expression classification. Unlike iterative learning algorithms, our hybrid approach analytically determines the framework learning parameters and captures the diversity of network behaviors from the learning function by using wavelets with different parameters in each of the fuzzy rules. Finally, this study aims to contribute a new facial expression dataset to the literature. The rest of the paper can be summarized as follows: In Section 2, we briefly recall the KELM and FWNN algorithms and then show the mathematical structure of our hybrid approach. In this context, we show the equivalence of a KELM with an FW model by using the proof of the theorem that the Mexican hat wavelet is an admissible ELM kernel. In the hybrid algorithm, all fuzzy rules consist of the IF-THEN structure and the algorithm uses the sigmoid activation function and the Mexican hat wavelet kernel function, respectively. In Section 3, to evaluate the performance of the hybrid algorithm, we present the experiments we designed, the datasets we used, the results of the experiments, and the comparison results with classical baseline methods to evaluate the performance of the hybrid model. In Section 4, all findings are discussed, and recommendations for future studies are made in Section 5.