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Applications and Comparison

PNN algorithm is aimed to extract knowledge from observation and experimental data and to determine its best mathematical description. PNN - a self-organizing multi-layered iterative algorithm that automatically provides linear and non-linear 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 non-linear 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 on-line 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 GMDH-type 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 non-linear 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. GMDH-type 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 on-line calculations
Here you may get on-line 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 GMDH-type 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 feed-forward artificial neural networks can be used to model complex non-linear 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 short-term 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 long-time 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    