Pi-Sigma Neural Network Research Articles

An Improved Pi-Sigma Neural Network with Error Feedback for Physical Time Series Prediction

An Improved Pi-Sigma Neural Network with Error Feedback for Physical Time Series Prediction

MULTIPLICATIVE NEURON MODEL BASED ON SINE COSINE ALGORITHM FOR TIME SERIES PREDICTION

Time series prediction is a method to predict the system behavior in the future based on current given data. Neural Networks (NNs) approach is a well-known technique that is useful for time series prediction. In the literature many NN models such Multilayer Perceptron (MLP), Pi-Sigma NN (PSNN), Recurrent NN etc. are proposed for solving time series prediction. In this paper, we use Multiplicative Neuron Model (MNM) to predict time series. For training this model, we propose use newly developed evolutionary optimization algorithm called Sine Cosine algorithm (SCA), and this algorithm has not been used as far as we know in training the MNM. The proposed SCA-MNM model is employed for the most known time series problems. In this paper, the application of the SCA-MNM on time prediction is illustrated using two mostly used datasets Mackey-Glass time series dataset, Box-Jenkins gas furnace dataset. To investigate the effect of the proposed SCA-MNM model, comparisons were made with some of the results given in the literature.

Intuitionistic time series fuzzy inference system

Although adaptive network fuzzy inference system and fuzzy functions approach can be utilized as a prediction tool, they have been not designed for prediction problem and they ignore the dependency structure of time series observations. From this viewpoint, making a design of the method that considers the dependency structure of observations will provide to get more accurate prediction. In this study, an intuitionistic time series fuzzy inference system (I-TSFIS) has been proposed. In the I-TSFIS, in just the same way as in the intuitionistic fuzzy inference systems, not only the membership values and crisp observations but also the non-membership values are used as inputs. Moreover, due to the use of crisp values as targets and outputs, the output does not need to be deffuzzified. Non-linear relationships between inputs and outputs of the proposed I-TSFIS are determined by Sigma-Pi neural network (SP-NN). The obtaining of optimal weights of SP-NN is performed by modified particle swarm optimization. And also I-TSFIS uses intuitionistic fuzzy C-means to obtain fuzzy clusters, membership and non-membership values of observations for these clusters. To evaluate the prediction performance of the proposed I-TSFIS, various real-life time series data sets have been analyzed and the results demonstrate the superior prediction ability of the proposed I-TSFIS.

Design, Implementation, and Evaluation of a Neural-Network-Based Quadcopter UAV System

In this paper, a quadcopter unmanned aerial vehicle (UAV) system based on neural-network enhanced dynamic inversion control is proposed for multiple real-world application scenarios. A sigma-pi neural network (SPNN) is used as the compensator to reduce the model error and improve the system performance in the presence of the uncertainties of UAV dynamics, payload, and environment. Besides, we present a technical framework for fast and robust implementation of multipurpose UAV systems and develop a testbed for the evaluation of UAV control system by using a high-precision optical motion capture system. Both simulation results and experiment results demonstrate that the SPNN can reduce the inversion errors related to UAV parameter uncertainties as well as tracking errors related to unknown disturbances and unmodeled dynamics. With the help of an online neural network (NN) learning mechanism, the entire system can achieve much higher accuracy in attitude and trajectory control than that achieved by conventional proportional-integral derivative based control systems under varying flight conditions.

Utility of a Shuffled Differential Evolution algorithm in designing of a Pi-Sigma Neural Network based predictor model

Since the last few decades, Artificial Neural Networks have been the center of attraction of a large number of researchers for solving diversified problem domains. Due to its distinguishing features such as generalization ability, robustness and strong ability to tackle nonlinear problems, it appears to be more popular in financial time series modeling and prediction. In this paper, a Pi-Sigma Neural Network is designed for foretelling the future currency exchange rates in different prediction horizon. The unrevealed parameters of the network are interpreted by a hybrid learning algorithm termed as Shuffled Differential Evolution (SDE). The main motivation of this study is to integrate the partitioning and random shuffling scheme of Shuffled Frog Leaping algorithm with evolutionary steps of a Differential Evolution technique to obtain an optimal solution with an accelerated convergence rate. The efficiency of the proposed predictor model is actualized by predicting the exchange rate price of a US dollar against Swiss France (CHF) and Japanese Yen (JPY) accumulated within the same period of time.

Research on Adaptive Trajectory Tracking Algorithm for a Quadrotor Based on Backstepping and the Sigma-Pi Neural Network

In this paper, adaptive tracking control is applied to improve performances of an underactuated quadrotor helicopter with respect to attitude and position control. Firstly, the dynamic model is presented. Then a new trajectory tracking algorithm is designed by using the sigma-pi neural network and backstepping. The paper designs the sigma-pi neural network compensation control law and gives the Lyapunov-type stability analysis. Then the corresponding numerical simulations are performed by using MATLAB. Simulation results are shown to demonstrate the effectiveness of the proposed control strategy, which could reduce tracking error, decrease tracking time, and improve the anti-interference ability of the system.

A Novel Honey-Bees Mating Optimization Approach with Higher order Neural Network for Classification

In the recent past, several biological and natural phenomena have extensively attracted researchers towards the rapid development of science and engineering. Basically solving the optimization problems in various Engineering discipline is a popular topic among the other problem solving strategies. Most of the biological processes include the swarm intelligence research areas where the activity and the behavior of real insects have been studied. One of the recently developed Swarm algorithms is the Honey Bee Mating Optimization (HBMO) algorithm which is based on the mating behavior of bees. In this work, a hybrid metaheuristic honey bee mating based Pi-Sigma Neural Network (PSNN) have been proposed to successfully solve the classification problem of data mining. The proposed approach combines HBMO with the PSNN and is compared with other techniques like GA (Genetic Algorithm), DE (Differential Evolution), and PSO (Particle Swarm Optimization). Experimental results reveal that the proposed approach is steady as well as reliable and provides better classification accuracy than others.

Gold price prediction using an evolutionary pi-sigma neural network

Gold Price Prediction has always been a fascinating area of study for researchers and decision makers who wish to determine its future value efficiently and accurately. In this study a predictor model is designed using a Pi-Sigma Neural Network (PSNN) for prediction of future gold price. Two evolutionary estimation paradigms such as Particle Swarm Optimization (PSO) and Differential Evolution (DE) are suggested during training step of the Pi-Sigma Neural Network to optimize the tunable weights of the network. The model is evaluated based on certain performance evaluation criteria such as Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) over two dataset such as Gold/INR and Gold/AED accumulated within the same period of time. The result analysis illustrates the better prediction

A new fuzzy inference system for time series forecasting and obtaining the probabilistic forecasts via subsampling block bootstrap

Recent years, fuzzy inference systems have been commonly used for time series forecasting. It is well known that fuzzy inference systems can produce good forecasting. Although fuzzy inference systems like adaptive network fuzzy inference system have been preferred by many of researchers, these systems have many of problems. If data set contains many explanatory variables, the number of rules will increase dramatically. Classical fuzzy inference systems need to estimate too many parameters for a reasonable forecasting performance. In this study, a new fuzzy inference system is proposed for time series forecasting. The proposed inference system uses fuzzy c-means method for clustering and pi-sigma neural network for fuzzy modelling. Moreover, the proposed system can generate probabilistic outputs (forecasts) under favour of subsampling block bootstrap method. The performance of the proposed method was investigated by using some data sets. It is understood that the proposed inference system can produce better forecast results.

A fireworks algorithm based Pi-Sigma neural network (FWA-PSNN) for modelling and forecasting chaotic crude oil price time series

Capturing the complex correlations among the data on the crude oil price time series is challenging, hence accurate prediction of it is difficult. Contrast to multilayer artificial neural network, Pi-Sigma neural network (PSNN) is characterized with stronger approximation ability, fast learning and higher fault tolerance. Fireworks algorithm (FWA) is a new metaheuristic motivated from the occurrence of fireworks explosion, characterized with fast convergence capability, parallelism and finds global optima. This article intends to achieve the synergetic effect of both on hybridizing them. It uses FWA for optimization of weight and bias of PSNN (FWA-PSNN) and overcomes the limitations of gradient based training. It has single hidden layer structure and trainable weight, hence fast and robust. The FWA-PSNN is evaluated on prediction of crude oil price time series. Extensive simulation results, performance analysis, and statistical significance test suggested the suitability of FWA-PSNN.

High order fuzzy time series method based on pi-sigma neural network

Fuzzy time series methods, which do not require the strict assumptions of classical time series methods, generally consist of three stages as fuzzification of crisp time series observations, determination of fuzzy relationships and defuzzification. All of these stages play a very important role on the forecasting performance of the model. An important stage of the fuzzy time series analysis is to determine the fuzzy relationships. Artificial neural networks seem to be very effective in determining fuzzy relationships that improve the accuracy of the forecasting performance. Several neuron models with different characteristics have been proposed so far. One of these models is Pi-Sigma neural network. An important advantage of Pi-Sigma neural network is that it requires fewer weights and nodes and has a lower number of computations when compared to multilayer perceptron. In this study, a new model for determining the fuzzy relationships for high order fuzzy time series forecasting which uses Pi-Sigma neural network is introduced. A modified particle swarm optimization model is used to train the Pi-Sigma network. We test the new model on two real datasets and we also perform a simulation study. The results are compared to the ones obtained by other techniques and show a better performance.

Median-Pi artificial neural network for forecasting

Datasets with outliers can be predicted with robust learning methods or robust artificial neural networks. In robust artificial neural networks, the architectures become robust by using robust statistics as aggregation functions. Median neural network and trimmed mean neural network are two robust artificial neural networks used in the literature. In these robust artificial neural networks, median and trimmed mean statistics are used as aggregation functions. In this study, Median-Pi artificial neural network is proposed as a new robust neural network for the purpose of forecasting. In Median-Pi artificial neural network, median and multiplicative functions are used as aggregation functions. Because of using median, the proposed network can produce good results for data with outliers. The Median-Pi artificial neural network is trained by particle swarm optimization. The performance of the neural network is investigated by using datasets from the International Time Series Forecast Competition 2016 (CIF-2016). The performance of the proposed method in case of outlier is compared to some other artificial neural networks. Median neural network, trimmed mean neural network, Pi-Sigma neural network and the proposed robust network are applied to time series with outlier, and the obtained results are compared. According to application results, the proposed Median-Pi artificial neural network can produce better forecast results than the other network types.

Elitist teaching–learning-based optimization (ETLBO) with higher-order Jordan Pi-sigma neural network: a comparative performance analysis

This paper presents the performance analysis of a newly developed elitist teaching–learning-based optimization algorithm applied with an efficient higher-order Jordan Pi-sigma neural network (JPSNN) for real-world data classification. Teaching–learning-based optimization (TLBO) algorithm is a recent metaheuristic, which is inspired through the teaching and learning process of both teacher and learner. As compared to other algorithms, it is efficient and robust due to its non-controlling parameter adjustments feature. Elitist TLBO is an improved version of TLBO with the addition of elitist solutions, which makes it more efficient. During the experiment, first the TLBO and then ETLBO algorithm are applied with only Pi-sigma neural network and its performance has been compared with other methods such as GA and PSO. Then, the ETLBO algorithm is applied with JPSNN and found better results over other methods. The proposed method has been tested with real-world benchmark datasets considered from UCI machine learning repository, and the performance has been compared with all seven approaches along with other HONN to prove the effectiveness of the method. Simulation results and statistical analysis show the superiority in the performance of the proposed approach as well as prove the potentiality over other existing approaches.

Chaotic Time Series Forecasting Using Higher Order Neural Networks

This study presents a novel application and comparison of higher order neural networks (HONNs) to forecast benchmark chaotic time series. Two models of HONNs were implemented, namely functional link neural network (FLNN) and pi-sigma neural network (PSNN). These models were tested on two benchmark time series; the monthly smoothed sunspot numbers and the Mackey-Glass time-delay differential equation time series. The forecasting performance of the HONNs is compared against the performance of different models previously used in the literature such as fuzzy and neural networks models. Simulation results showed that FLNN and PSNN offer good performance compared to many previously used hybrid models.

Autopilot design for tilt-rotor unmanned aerial vehicle with nacelle mounted wing extension using single hidden layer perceptron neural network

Single hidden layer perceptron neural network controllers combined with dynamic inversion are applied to the tilt-rotor unmanned aerial vehicle and its variant model with the nacelle mounted wing extension. The bandwidths of the inner loop and outer loop of the controller are designed using the timescale separation approach, which uses the combined analysis of the two loops. The bandwidth of each loop is selected to be close to each other using a combination of the pseudo-control-hedging and the pole-placement method. Similar to the previous studies on sigma-pi neural network, the dynamic inversion at hover conditions of the original tilt-rotor model is used as a baseline for both aircraft, and the compatible solution to the Lyapunov equation is suggested. The single hidden layer perceptron neural network minimizes the error of the inversion model through the back-propagation adaptation. The waypoint guidance is applied to the outermost loop of the neural network controller for autonomous flight which includes vertical take-off and landing as well as nacelle conversion. The simulation results under the two wind conditions for the tilt-rotor aircraft and its variant are presented. The south and north-west wind directions are simulated in order to compare with the results from the existing sigma-pi neural network, and the estimation results of the wind are presented.

Batch Gradient Method for Training of Pi-Sigma Neural Network with Penalty

Batch Gradient Method for Training of Pi-Sigma Neural Network with Penalty

Solving nonlinear classification problems with black hole optimisation and higher order Jordan Pi-sigma neural network: a novel approach

Nature inspired optimisation algorithms have been on a leading focus of all researchers since last few decades. Successful applications of such algorithms for solving diversified problem domains make them more popular. This presented research is about to implement a novel nature inspired algorithm with higher order neural network for solving nonlinear classification problems of data mining. A recently developed nature inspired algorithm, black hole optimisation has been used to train the weights of a higher order Jordan Pi-sigma neural network and to optimise the performance of the network. The proposed black hole algorithm-based higher order neural network has been developed for solving the classification problems in data mining. The result of the proposed method is compared with some other benchmark meta-heuristic techniques like PSO, GA and found that the proposed method is superior to other approaches.

Solving nonlinear classification problems with black hole optimisation and higher order Jordan Pi-sigma neural network: a novel approach

Solving nonlinear classification problems with black hole optimisation and higher order Jordan Pi-sigma neural network: a novel approach

Fluctuation prediction of stock market index by adaptive evolutionary higher order neural networks

The stock market is complex and dynamic in nature, and has been a subject of research for modelling its random fluctuations. Higher order neural network (HONN) has the ability to expand the input representation space, perform high learning capabilities and have been utilised to solve many complex data mining problems. To capture the extreme volatility, nonlinearity and uncertainty associated with stock data, this paper compares two adaptive evolutionary optimisation-based Pi-Sigma neural networks (AE-PSNN), for prediction of closing prices of five real stock markets. For this experimental study, BSE, DJIA, NASDAQ, FTSE and TAIEX stock indices are employed for short, medium and long term predictions. The performance of the AE-PSNN models has been compared with that of a gradient descent-based PSNN (GD-PSNN) model and found to be superior in terms of prediction accuracy and prediction of change in direction.

A novel Chemical Reaction Optimization based Higher order Neural Network (CRO-HONN) for nonlinear classification

In this paper, a Chemical Reaction Optimization (CRO) based higher order neural network with a single hidden layer called Pi–Sigma Neural Network (PSNN) has been proposed for data classification which maintains fast learning capability and avoids the exponential increase of number of weights and processing units. CRO is a recent metaheuristic optimization algorithm inspired by chemical reactions, free from intricate operator and parameter settings such as other algorithms and loosely couples chemical reactions with optimization. The performance of the proposed CRO-PSNN has been tested with various benchmark datasets from UCI machine learning repository and compared with the resulting performance of PSNN, GA-PSNN, PSO-PSNN. The methods have been implemented in MATLAB and the accuracy measures have been tested by using the ANOVA statistical tool. Experimental results show that the proposed method is fast, steady and reliable and provides better classification accuracy than others.