Applications and Comparison
PNN algorithm is aimed to extract knowledge from observation and
experimental data and to determine its best mathematical description. PNN  a
selforganizing multilayered iterative algorithm that automatically provides
linear and nonlinear polynomial regression models. The PNN embodies the
advantages Multiple Linear Regression (MLR) and Artificial Neural Networks
(ANNs) into a single entity. It can model both linear and nonlinear
relationships like ANNs, and it yields a polynomial regression equation like
MLR for easy interpretation. This algorithm provides robust results in the
presence of correlated and irrelative variables or/and outliers. The results of
this algorithm can be easily interpreted.




General
description 





Article:
«Polynomial Neural Network algorithms» >>> 





PNN
online calculations >>> 





PNN
in drug design 





PNN
in stock market prediction 

General
description
Polynomial Neural Network (PNN) provides robust nonlinear polynomial regression
identification for the numerical data with unknown dependencies. It is based on
modified
GMDHtype Neural Networks and characterized by the highest prediction
ability. Moreover it is insensible to outliers and irrelevant variables,
provides fast learning and numerical stability.
Let's compare PNN with Artificial Neural Network (ANN) algorithms, which also
can be used to model complex nonlinear relationship. The serious disadvantage
of ANN method is that the all dependencies (between parameters and responses)
are hidden within neural network structure and therefore the interpretation of
calculated results is difficult. Besides that an essential time of learning
make difficulties for using ANN in real time system for modeling and
forecasting. GMDHtype Neural Networks allows restoring the unknown nonlinear
regression in parametric form (as an equation). But original GMDH algorithms in
general rather sensitive to outliers. Methods of robust modeling insensitive to
outliers was developed in the linear case only and characterized by significant
time of calculation when the structure of model is unknown a priory.
Polynomial Neural Network

Allows identifying robust nonlinear polynomial models of unknown structure

Is insensible to outliers

Is characterized by numerical stability and high speed of learning that allows
using in real time system
Article:
«Polynomial Neural Network algorithms»
Let us consider basic principles of Polynomial Neural Network (PNN) algorithm
organization. The proposed method can be used to analyze complex data sets with
the aim to determine internal data relationships and to present knowledge about
these relationships in the form of mathematical description (polynomial
regression).
As an examples of possible application area of PNN algorithm one can consider
any sphere where sets of observation data should be analyzed and data
relationships models should be build. There are, for example, chemistry (QSAR),
economical systems analyses, stocks and financial market instruments, insurance
risks study, medical diagnostics, etc. More
>>>
PNN
online calculations
Here you may get online access to the PNN calculation server and analyse own
data or custom test sets. To get idea about input/output data and system
configuration, please, review the article Polynomial
Neural Network algorithms
Numerical
methods of drug design
Polynomial Neural Network (PNN) in drug design provides the identification of
robust nonlinear polynomial model in quantitative  structure activity
relationship (QSAR) studies. PNN is based on modified GMDHtype Neural
Networks, insensible to outliers and irrelevant variables, provides fast
leaning, numerical stability and characterized by high prediction ability for
the QSAR tasks.
The QSAR studies represent an important part of the drug design process and are
used to detect relationships between chemical structure of compounds and their
biological activities. The choice of algorithm depends on the specificity of
the problem to be solved. The specific features of the QSAR tasks can be
summarized as follows: there is large number of input variables; some of these
variables can be irrelevant and highly correlated. Multiple linear regression
analysis (MLRA) is widely used in QSAR because of the rather simple way to
interpret the results. The power of MLRA can be significantly increased if it
is combined with evolutionary algorithm. Other widespread method in QSAR study,
the partial least squares (PLS) method that represents a generalized regression
method based on latent vectors. However, both MLRA and PLS methods are limited
to linear regression models. The PLS algorithm is also sensitive to outliers or
irrelevant variables. Contrary to these methods, the feedforward artificial
neural networks can be used to model complex nonlinear relationship. However,
a serious disadvantage of this method is that the dependencies detected between
parameters and responses are hidden within neural network structure and
therefore the interpretation of calculated results is difficult. While the
traditional GMDH approaches provide the linear and nonlinear polynomial models
in parametric form and are well suited to solve QSAR problems, their results
are sensitive to outliers, not stable enough and, as a rule, cannot be easily
interpreted. Robust Polynomial Neural Network provides robust linear and
nonlinear modeling in the presence of outliers or/and correlated and irrelative
variables. It allows controlling the complexity  number and the maximal power
of terms in the models. The algorithm calculates the stable results in the form
of equation that can be easily interpreted.
Stock
market prediction
Polynomial Neural Networks (PNN) for stock market prediction.
Automatic system for shortterm prediction of the cost of financial instruments
(money, stocks, etc.) and decision making in the automatic trading system based
on numerical analysis of time series employed the PNN. It holds resources for
real time nonlinear modeling and characterized by high speed and insensibility
to outliers and irrelevant variables.
Nowadays the linear models are used for prediction of the financial instruments
by autoregressive modeling. The nonlinear methods are not used because of slow
learning that lead to almost insuperable problems employing them to real time
systems. Besides that linear models require the longtime observation for model
identification. High variability of market during that time doesn't allow
achieving the desired accuracy.
PNN algorithm

Allows restoring the linear as well as the nonlinear models of financial
instruments

Is characterized by high speed of leaning and realized in a real time system

Achieves the necessary accuracy considering the essentially shorter the
interval of observation

Is robust to outliers in the data
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