Functional networks and applications: A survey

Functional extreme learning machine

Introduction

Extreme learning machine (ELM) is a training algorithm for single hidden layer feedforward neural network (SLFN), which converges much faster than traditional methods and yields promising performance. However, the ELM also has some shortcomings, such as structure selection, overfitting and low generalization performance.

Methods

This article a new functional neuron (FN) model is proposed, we takes functional neurons as the basic unit, and uses functional equation solving theory to guide the modeling process of FELM, a new functional extreme learning machine (FELM) model theory is proposed.

Results

The FELM implements learning by adjusting the coefficients of the basis function in neurons. At the same time, a simple, iterative-free and high-precision fast parameter learning algorithm is proposed.

Discussion

The standard data sets UCI and StatLib are selected for regression problems, and compared with the ELM, support vector machine (SVM) and other algorithms, the experimental results show that the FELM achieves better performance.

Functional extreme learning machine for regression and classification

Although Extreme Learning Machine (ELM) can learn thousands of times faster than traditional slow gradient algorithms for training neural networks, ELM fitting accuracy is limited. This paper develops Functional Extreme Learning Machine (FELM), which is a novel regression and classifier. It takes functional neurons as the basic computing units and uses functional equation-solving theory to guide the modeling process of functional extreme learning machines. The functional neuron function of FELM is not fixed, and its learning process refers to the process of estimating or adjusting the coefficients. It follows the spirit of extreme learning and solves the generalized inverse of the hidden layer neuron output matrix through the principle of minimum error, without iterating to obtain the optimal hidden layer coefficients. To verify the performance of the proposed FELM, it is compared with ELM, OP-ELM, SVM and LSSVM on several synthetic datasets, XOR problem, benchmark regression and classification datasets. The experimental results show that although the proposed FELM has the same learning speed as ELM, its generalization performance and stability are better than ELM.

Soft Computing Applications in Air Quality Modeling: Past, Present, and Future

Air quality models simulate the atmospheric environment systems and provide increased domain knowledge and reliable forecasting. They provide early warnings to the population and reduce the number of measuring stations. Due to the complexity and non-linear behavior associated with air quality data, soft computing models became popular in air quality modeling (AQM). This study critically investigates, analyses, and summarizes the existing soft computing modeling approaches. Among the many soft computing techniques in AQM, this article reviews and discusses artificial neural network (ANN), support vector machine (SVM), evolutionary ANN and SVM, the fuzzy logic model, neuro-fuzzy systems, the deep learning model, ensemble, and other hybrid models. Besides, it sheds light on employed input variables, data processing approaches, and targeted objective functions during modeling. It was observed that many advanced, reliable, and self-organized soft computing models like functional network, genetic programming, type-2 fuzzy logic, genetic fuzzy, genetic neuro-fuzzy, and case-based reasoning are rarely explored in AQM. Therefore, the partially explored and unexplored soft computing techniques can be appropriate choices for research in the field of air quality modeling. The discussion in this paper will help to determine the suitability and appropriateness of a particular model for a specific modeling context.