A single dendritic neuron model (DNM) that owns the nonlinear information processing ability of dendrites has been widely used for classification and prediction. Complex-valued neural networks that consist of a number of multiple/deep-layer McCulloch-Pitts neurons have achieved great successes so far since neural computing was utilized for signal processing. Yet no complex value representations appear in single neuron architectures. In this article, we first extend DNM from a real-value domain to a complex-valued one. Performance of complex-valued DNM (CDNM) is evaluated through a complex XOR problem, a non-minimum phase equalization problem, and a real-world wind prediction task. Also, a comparative analysis on a set of elementary transcendental functions as an activation function is implemented and preparatory experiments are carried out for determining hyperparameters. The experimental results indicate that the proposed CDNM significantly outperforms real-valued DNM, complex-valued multi-layer perceptron, and other complex-valued neuron models.

Financial bankruptcy prediction is crucial for financial institutions in assessing the financial health of companies and individuals. Such work is necessary for financial institutions to establish effective prediction models to make appropriate lending decisions. In recent decades, various bankruptcy prediction models have been developed for academics and practitioners to predict the likelihood that a loan customer will go bankrupt. Among them, Artificial Neural Networks (ANNs) have been widely and effectively applied in bankruptcy prediction. Inspired by the mechanism of biological neurons, we propose an evolutionary pruning neural network (EPNN) model to conduct financial bankruptcy analysis. The EPNN possesses a dynamic dendritic structure that is trained by a global optimization learning algorithm: the Adaptive Differential Evolution algorithm with Optional External Archive (JADE). The EPNN can reduce the computational complexity by removing the superfluous and ineffective synapses and dendrites in the structure and is simultaneously able to achieve a competitive classification accuracy. After simplifying the structure, the EPNN can be entirely replaced by a logic circuit containing the comparators and the logic NOT, AND, and OR gates. This mechanism makes it feasible to apply the EPNN to bankruptcy analysis in hardware implementations. To verify the effectiveness of the EPNN, we adopt two benchmark datasets in our experiments. The experimental results reveal that the EPNN outperforms the Multilayer Perceptron (MLP) model and our previously developed preliminary pruning neural network (PNN) model in terms of accuracy, convergence speed, and Area Under the Receiver Operating Characteristics (ROC) curve (AUC). In addition, the EPNN also provides competitive and satisfactory classification performances in contrast with other commonly used classification methods.

A dendritic neuron model with adaptive synapses (DMASs) based on differential evolution (DE) algorithm training is proposed. According to the signal transmission order, a DNM can be divided into four parts: the synaptic layer, dendritic layer, membrane layer, and somatic cell layer. It can be converted to a logic circuit that is easily implemented on hardware by removing useless synapses and dendrites after training. This logic circuit can be designed to solve complex nonlinear problems using only four basic logical devices: comparators, AND (conjunction), OR (disjunction), and NOT (negation). To obtain a faster and better solution, we adopt the most popular DE for DMAS training. We have chosen five classification datasets from the UCI Machine Learning Repository for an experiment. We analyze and discuss the experimental results in terms of the correct rate, convergence rate, ROC curve, and the cross-validation and then compare the results with a dendritic neuron model trained by the backpropagation algorithm (BP-DNM) and a neural network trained by the backpropagation algorithm (BPNN). The analysis results show that the DE-DMAS shows better performance in all aspects.

This article presents a triple‐valued gravitational search algorithm (TGSA) to tackle the graph planarization problem (GPP). GPP is one of the most important tasks in graph theory, and has proved to be an NP‐hard problem. To solve it, TGSA uses a triple‐valued encoding scheme and models the search space into a triangular hypercube quantitatively based on the well‐known single‐row routing representation method. The agents in TGSA, whose interactions are driven by the gravity law, move toward the global optimal position gradually. The position updating rule for each agent is based on two indices: one is avelocity indexwhich is a function of the current velocity of the agent, and the other is apopulation indexbased on the cumulative information in the whole population. To verify the performance of the algorithm, 21 benchmark instances are tested. Experimental results indicate that TGSA can solve the GPP by finding its maximum planar subgraph and embedding the resulting edges into a plane simultaneously. Compared with traditional algorithms, a novelty of TGSA is that it can find multiple optimal solutions for the GPP. Comparative results also demonstrate that TGSA outperforms the traditional meta‐heuristics in terms of the solution qualities within reasonable computational times. Published by John Wiley & Sons, Inc.