Volterra Neural Network Research Articles

Latent code-based fusion: A Volterra neural network approach

We propose a deep structure encoder using Volterra Neural Networks (VNNs) to seek a latent representation of multi-modal data whose features are jointly captured by a union of subspaces. The so-called self-representation embedding of the latent codes leads to a simplified fusion which is driven by a similarly constructed decoding. The Volterra Filter architecture achieved reduction in parameter complexity is primarily due to controlled non-linearities being introduced by the higher-order convolutions in lieu of generalized activation functions. Experimental results on two different datasets have shown a significant improvement in the clustering performance for VNNs auto-encoder over conventional Convolutional Neural Networks (CNNs) auto-encoder. In addition, we also show that the proposed approach demonstrates a much-improved sample complexity over CNN-based auto-encoder with a robust classification performance.

Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network

Identification of nonlinear discrete systems using a new Hammerstein model with Volterra neural network

Conquering the CNN Over-Parameterization Dilemma: A Volterra Filtering Approach for Action Recognition

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filtering so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this Volterra Neural Network (VNN), along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art CNN approaches.

The Advanced Algorithmic Method for Navigation System Correction of Spacecraft

In this paper an advanced method for the navigation system correction of a spacecraft using an error prediction model of the system is proposed. Measuring complexes have been applied to determine the parameters of a spacecraft and the processing of signals from multiple measurement systems is carried out. Under the condition of interference in flight, when the signals of external system (such as GPS) disappear, the correction of navigation system in autonomous mode is considered to be performed using an error prediction model. A modified Volterra neural network based on the self-organization algorithm is proposed in order to build the prediction model, and the modification of algorithm indicates speeding up the neural network. Also, three approaches for accelerating the neural network have been developed; two examples of the sequential and parallel implementation speed of the system are presented by using the improved algorithm. In addition, simulation for a returning spacecraft to atmosphere is performed to verify the effectiveness of the proposed algorithm for correction of navigation system.

Fetal cardiotocography monitoring using Legendre neural networks.

A new technique for electronic fetal monitoring (EFM) using an efficient structure of neural networks based on the Legendre series is presented in this paper. Such a structure is achieved by training a Legendre series-based neural network (LNN) to classify the different fetal states based on recorded cardiotocographic (CTG) data sets given by others. These data sets consist of measurements of fetal heart rate (FHR) and uterine contraction (UC). The applied LNN utilizes a Legendre series expansion for the input vectors and, hence, has the capability to produce explicit equations describing multi-input multi-output systems. Simulations of the proposed technique in EFM demonstrate its high efficiency. Training the LNN requires a few number of iterations (5-10 epochs). The applied technique makes the classification of the fetal state available through equations combining the trained LNN weights and the current measured CTG record. A comparison of performance between the proposed LNN and other popular neural network techniques such as the Volterra neural network (VNN) in EFM is provided. The comparison shows that, the LNN outperforms the VNN in case of less computational requirements and fast convergence with a lower mean square error.

VOLTERRA NEURAL NETWORK CONSTRUCTION IN THE NONLINEARDYNAMIC SYSTEMS MODELING PROBLEM

The features of using the theory of Volterraseries and neural networks in problems of nonlinear dynamic systems model-ing are considered.A comparative analysis of methods for constructing models of nonlinear dynamic systems based on the theory of Volterra series and neural networks is carried out;areas of effective application of each method are indicated. The problem statementis formulated, consisting in the creation of a mathematical apparatus for transforming models of nonlinear dynamic systems derived from the Volterra series apparatus into an artificial neural network of a certain structure.The three-layer structure of a direct signal propa-gation neural network has been substantiated and investigated forrepresent nonlinear dynamic systems. It is outlined a class of systems that can be efficiently approximated by this network.The dependence of the Volterra kernelscoefficients and the weighting coefficients of the hidden layer of the three-layer forward-propagation neural network is established.An algorithm for constructing an artificial neural network based on the Volterra series is given.The results of computer simulation of nonlinear dynamic systems using the Volterra neural network and direct signal propagation neural network are presented. The analysis of experimental data confirms theeffectiveness of using Volterraneural networks in problems of modeling nonlinear dynamic systems.Conclusions and recommendations on the effec-tive use of Volterra neural networks for modeling nonlinear dynamic systems are made.

Application of neural network and genetic algorithm in identification of a model of a variable mass underwater vehicle

This paper is one of the few works in identification of a model of a Variable Mass Underwater Vehicles (VMUVs) with six degrees of freedom. Since, the mass of fuel changes during the operation, the mass and the center of mass of these vehicles also change and therefore the VMUV has nonlinear-time varying model. In order to obtain a model of the VMUV, an identification procedure is done by using an especial neural network. In this network, which is called the Volterra neural network, the basis functions are Volterra polynomials. Also, genetic algorithm (GA) is used with neural network to structure selection of these nonlinear polynomials. Computer simulations, Monte Carlo and cross-correlation analyses are done by considering admissible levels of noises in the underwater vehicles instrumentations (rate gyros) and the results show the efficiency of the presented approach.

Multi-step Prediction Algorithm of Traffic Flow Chaotic Time Series Based on Volterra Neural Network

The accurate traffic flow time series prediction is the prerequisite for achieving traffic flow inducible system. Aiming at the issue about multi-step prediction traffic flow chaotic time series, the traffic flow Volterra Neural Network (VNN) rapid learning algorithm is proposed. Combing with the chaos theory and the Volterra functional analysis, method of the truncation order and the truncation items is given and the VNN model of traffic flow time series is built. Then the mechanism of the chaotic learning algorithm is described, and the adaptive learning algorithm of VNN for traffic flow time series is designed. Last, a multi-step prediction of traffic flow chaotic time series is researched by traffic flow VNN network model, Volterra prediction filter and the BP neural network based on chaotic algorithm. The simulations show that the VNNTF network model predictive performance is better than the Volterra prediction filter and the BP neural network by the simulation results and root-mean-square value.

Modeling Induction Motors

Abstract: In this paper, a novel technique for on-line estimation of most electrical parameters of an induction motor is presented. Such estimation is important to achieve high performance drive systems. The proposed technique uses Volterra neural networks (VNN). This technique is based on the measurements of the stator voltages, currents and motor speed with no need for state-space modeling. Moreover, the VNN is implemented to relate the steadystate performance characteristics of an induction motor to their inputs. Simulation and practical results establish the validity of the proposed technique and show reasonable accuracy of the estimated parameters as well as excellent steady-state performance characteristics.

Solving TSP by using Lotka–Volterra neural networks

This paper proposes a new approach to solve traveling salesman problem (TSP) by using a class of Lotka–Volterra neural networks (LVNN) with global inhibition. Some stability criteria that ensure the convergence of valid solutions are obtained. It is proved that an equilibrium state is stable if and only if it corresponds to a valid solution of the TSP. Thus, a valid solution can always be obtained whenever the network convergence to a stable state. A set of analytical conditions for optimal settings of LVNN is derived. Simulation results illustrate the theoretical analysis.

A subthreshold MOS circuit for the Lotka–Volterra neural network producing the winners-share-all solution

An analog MOS circuit is proposed for implementing a Lotka–Volterra (LV) competitive neural network which produces winners-share-all solutions. The solutions give multiple winners receiving large inputs and are particularly useful for selecting a set of inputs through “decision by majority”. We show that the LV network can easily be implemented using subthreshold MOS transistors. Results of extensive circuit simulations prove that the proposed circuit does exhibit a reliable selection compared with winner-take-all circuits, in the possible presence of device mismatches. These results pave a way to future implementation on a real device.