Supervised Learning in Multilayer Spiking Neural Networks

The current article introduces a supervised learning algorithm for multilayer spiking neural networks. The algorithm presented here overcomes some limitations of existing learning algorithms as it can be applied to neurons firing multiple spikes and it can in principle be applied to any linearisable neuron model. The algorithm is applied successfully to various benchmarks, such as the XOR problem and the Iris data set, as well as complex classifications problems. The simulations also show the flexibility of this supervised learning algorithm which permits different encodings of the spike timing patterns, including precise spike trains encoding.Comment: 38 pages, 4 figure

Automatic Curve Fitting Based on Radial Basis Functions and a Hierarchical Genetic Algorithm

Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included

Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included

Embedded system implementation of an evolutionary algorithm for circle detection on programmable devices

Programmable devices combine powerful processing systems with a rich infrastructure of general-purpose and specific logic blocks, making it possible the efficient implementation of embedded systems to perform complex tasks by facilitating hardware acceleration of critical stages to improve their performance. Based on these characteristics, a hardware implementation of a genetic algorithm for circle detection in digital images is described in this paper. The detection system has been designed for Xilinx Zynq-7000 and Zynq UltraScale+ family devices and implemented on two low-cost development boards that reach acceleration factors of 33.12 and 37.3, respectively, when compared to the fully software implementation. Detection results from both development boards have been compared using synthetic and real images from different scenarios. The accuracy and performance achieved demonstrate the suitability of this proposal to design embedded systems with restricted size, resources and energy consumption for applications in Internet of Things, Industry 4.0 and other related paradigms.Luis F. Rojas-Munoz acknowledges conacyt for the support granted for the development of this research (Grant No. 718883).Peer reviewe

Quadrupedal Robot Locomotion: A Biologically Inspired Approach and Its Hardware Implementation

A bioinspired locomotion system for a quadruped robot is presented. Locomotion is achieved by a spiking neural network (SNN) that acts as a Central Pattern Generator (CPG) producing different locomotion patterns represented by their raster plots. To generate these patterns, the SNN is configured with specific parameters (synaptic weights and topologies), which were estimated by a metaheuristic method based on Christiansen Grammar Evolution (CGE). The system has been implemented and validated on two robot platforms; firstly, we tested our system on a quadruped robot and, secondly, on a hexapod one. In this last one, we simulated the case where two legs of the hexapod were amputated and its locomotion mechanism has been changed. For the quadruped robot, the control is performed by the spiking neural network implemented on an Arduino board with 35% of resource usage. In the hexapod robot, we used Spartan 6 FPGA board with only 3% of resource usage. Numerical results show the effectiveness of the proposed system in both cases

Multiple Active Contours Guided by Differential Evolution for Medical Image Segmentation

This paper presents a new image segmentation method based on multiple active contours guided by differential evolution, called MACDE. The segmentation method uses differential evolution over a polar coordinate system to increase the exploration and exploitation capabilities regarding the classical active contour model. To evaluate the performance of the proposed method, a set of synthetic images with complex objects, Gaussian noise, and deep concavities is introduced. Subsequently, MACDE is applied on datasets of sequential computed tomography and magnetic resonance images which contain the human heart and the human left ventricle, respectively. Finally, to obtain a quantitative and qualitative evaluation of the medical image segmentations compared to regions outlined by experts, a set of distance and similarity metrics has been adopted. According to the experimental results, MACDE outperforms the classical active contour model and the interactive Tseng method in terms of efficiency and robustness for obtaining the optimal control points and attains a high accuracy segmentation

Evolutionary Spiking Neural Networks for Solving Supervised Classification Problems

This paper presents a grammatical evolution (GE)-based methodology to automatically design third generation artificial neural networks (ANNs), also known as spiking neural networks (SNNs), for solving supervised classification problems. The proposal performs the SNN design by exploring the search space of three-layered feedforward topologies with configured synaptic connections (weights and delays) so that no explicit training is carried out. Besides, the designed SNNs have partial connections between input and hidden layers which may contribute to avoid redundancies and reduce the dimensionality of input feature vectors. The proposal was tested on several well-known benchmark datasets from the UCI repository and statistically compared against a similar design methodology for second generation ANNs and an adapted version of that methodology for SNNs; also, the results of the two methodologies and the proposed one were improved by changing the fitness function in the design process. The proposed methodology shows competitive and consistent results, and the statistical tests support the conclusion that the designs produced by the proposal perform better than those produced by other methodologies