The polynomial neural network

doi:10.1016/0020-0255(95)00133-6

Information Sciences

Volume 87, Issue 4, November 1995, Pages 231-246

https://doi.org/10.1016/0020-0255(95)00133-6 Get rights and content

Abstract

In this paper, we propose a new feedback neural network, called the polynomial neural network (PNN). This network offers several advantages over conventional feedback neural networks. Since it allows a second-order method of convergence to its memory locations, it approaches equilibrium rapidly. The memories of this network can be located anywhere in an n-dimensional space rather than being confined to the corners of a hypercube, as is the case with Hopfield and other networks that use sigmoidal or similar nonlinearities, such as Hopfield networks. The spurious states of this network are few and can be determined easily upon examination. Issues relating to the dynamic behavior of the PNN are addressed. A noniterative technique has been suggested to create desired memory locations in the network. Finally, the performance of the PNN is studied. The attraction basins of the network reveal a complex fractal-like topology. Whereas issues relating to the hardware realization of this network have only been addressed very briefly, it has been indicated that such a network would require a large amount of hardware for its realization. This problem can be obviated by using a simplified model, whose performance is comparable to that of the basic model while requiring much less hardware.

References (13)

P.G. Ciarit
An Introduction to Numerical Linear Algebra and Optimization
(1982)
R.L. Devaney
An Introduction to Chaotic Dynamical Systems
(1986)
D.O. Hebb
The Organization of Behavior
(1949)
J.J. Hopfield
Neural networks and physical systems with emergent collective computational abilities
J.J. Hopfield
Neurons with graded response have collective computational properties like two-state neurons
J.J. Hopfield et al.
Neural computation of decisions in optimization problems
Biol. Cybern.
(1985)

There are more references available in the full text version of this article.

Cited by (3)

Machine learning toward improving the performance of membrane-based wastewater treatment: A review
2023, Advanced Membranes
Machine learning (ML) is a data-driven approach that can be applied to design, analyze, predict, and optimize a process based on existing data. Recently, ML has found its application in improving membrane separation performance for wastewater treatment. Models have been developed to predict the performance of membranes to separate contaminants from wastewater, design optimum conditions for membrane fabrication for greater membrane separation performance and predict backwashing membranes and membrane fouling. This review summarizes the progress of ML-based membrane separation modeling and explores the direction of the future development of ML in membrane separation-based wastewater treatment. The strengths and drawbacks of the ML algorithms extensively used in membrane separation-based wastewater treatment are summarized. Artificial neural network (ANN) was the most used algorithm for modeling membrane separation-based wastewater treatment. Future research is recommended to focus on the development of integrated ML algorithms and on combining ML algorithms with other modeling approaches (e.g., process-based models and statistical models). This will serve to achieve higher accuracy and better performance of the ML application.
Constructing ordinary sum differential equations using polynomial networks
2014, Information Sciences
Data relations can define general sum partial differential equations of a composite function additive derivative model. Time-series data observations can analogously describe an ordinary sum differential equation with time derivatives, which is possible to be solved using partial derivative term substitutions of time-dependent series. Differential polynomial neural network is a new type of neural network, which constructs and substitutes for an unknown general partial differential equation from data observations, developed by the author. It generates sum series of convergent partial polynomial derivative terms, which can describe an unknown complex function time-series. This type of non-linear regression decomposes a system model, described by the general differential equation, into many partial low order derivative specifications of selected relative sum terms. Common soft-computing techniques in general can apply input variables of only absolute interval values of a specific data range. The character of relative data allows processing a wider range of test interval values than defined by a training set. The characteristics of the composite sum differential equation solutions can facilitate a much greater variety of model forms than is allowed using standard soft computing methods. Recurrent neural network proved to form simple solid time-series models, most of which it is possible to describe using ordinary differential equations, so the comparisons were done.
Multi-criterion Pareto based particle swarm optimized polynomial neural network for classification: A review and state-of-the-art
2009, Computer Science Review
Citation Excerpt :
Classification is one of the most studied tasks in Data Mining and Knowledge Discovery in Databases (DM and KDD) [1–7], pattern recognition [8–12], image processing [13–15] and bio-informatics [16–21]. In solving classification tasks, the classical algorithm such as PNN [22,23] and its variants [24] try to measure the performance by considering only one evaluation criterion, i.e. classification accuracy. However, one more important criterion like architectural complexity embedded in PNN is being completely ignored.
In this paper, we proposed a multi-objective Pareto based particle swarm optimization (MOPPSO) to minimize the architectural complexity and maximize the classification accuracy of a polynomial neural network (PNN). To support this, we provide an extensive review of the literature on multi-objective particle swarm optimization and PNN. Classification using PNN can be considered as a multi-objective problem rather than as a single objective one. Measures like classification accuracy and architectural complexity used for evaluating PNN based classification can be thought of as two different conflicting criterions. Using these two metrics as the criteria of classification problem, the proposed MOPPSO technique attempts to find out a set of non-dominated solutions with less complex PNN architecture and high classification accuracy. An extensive experimental study has been carried out to compare the importance and effectiveness of the proposed method with the chosen state-of-the-art multi-objective particle swarm optimization (MOPSO) algorithm using several benchmark datasets. A comprehensive bibliography is included for further enhancement of this area.

View full text

The polynomial neural network

Abstract

An Introduction to Numerical Linear Algebra and Optimization

An Introduction to Chaotic Dynamical Systems

The Organization of Behavior

Neural networks and physical systems with emergent collective computational abilities

Neurons with graded response have collective computational properties like two-state neurons

Neural computation of decisions in optimization problems

Biol. Cybern.