scholarly journals Recognition of Generalized Patterns by a Differential Polynomial Neural Network

2012 ◽  
Vol 2 (1) ◽  
pp. 167-172 ◽  
Author(s):  
L. Zjavka
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Differential Polynomial ◽  
Use Of Data ◽  
Polynomial Neural Network ◽  
Wide Range ◽  
Pattern Similarity ◽  
Generalized Patterns ◽  
Input Variables ◽  
Parametric Polynomials

A lot of problems involve unknown data relations, identification of which can serve as a generalization of their qualities. Relative values of variables are applied in this case, and not the absolute values, which can better make use of data properties in a wide range of the validity. This resembles more to the functionality of the brain, which seems to generalize relations of variables too, than a common pattern classification. Differential polynomial neural network is a new type of neural network designed by the author, which constructs and approximates an unknown differential equation of dependent variables using special type of root multi-parametric polynomials. It creates fractional partial differential terms, describing mutual derivative changes of some variables, likewise the differential equation does. Particular polynomials catch relations of given combinations of input variables. This type of identification is not based on a whole-pattern similarity, but only to the learned hidden generalized relations of variables.

scholarly journals Predictive modelling of soils’ hydraulic conductivity using artificial neural network and multiple linear regression

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Charles Gbenga Williams ◽  
Oluwapelumi O. Ojuri
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Hydraulic Conductivity ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Coarse Grained ◽  
Soil Types ◽  
Wide Range ◽  
Artificial Neural ◽  
Input Variables

AbstractAs a result of heterogeneity nature of soils and variation in its hydraulic conductivity over several orders of magnitude for various soil types from fine-grained to coarse-grained soils, predictive methods to estimate hydraulic conductivity of soils from properties considered more easily obtainable have now been given an appropriate consideration. This study evaluates the performance of artificial neural network (ANN) being one of the popular computational intelligence techniques in predicting hydraulic conductivity of wide range of soil types and compared with the traditional multiple linear regression (MLR). ANN and MLR models were developed using six input variables. Results revealed that only three input variables were statistically significant in MLR model development. Performance evaluations of the developed models using determination coefficient and mean square error show that the prediction capability of ANN is far better than MLR. In addition, comparative study with available existing models shows that the developed ANN and MLR in this study performed relatively better.

scholarly journals Generalization of Patterns by Identification with Polynomial Neural Network

2010 ◽  
Vol 61 (2) ◽  
pp. 120-124 ◽  
Author(s):  
Ladislav Zjavka
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Functional Dependence ◽  
Polynomial Neural Network ◽  
New Type ◽  
Input Variables ◽  
The Brain ◽  
Functional Output ◽  
Simplified Form

Generalization of Patterns by Identification with Polynomial Neural Network Artificial neural networks (ANN) in general classify patterns according to their relationship, they are responding to related patterns with a similar output. Polynomial neural networks (PNN) are capable of organizing themselves in response to some features (relations) of the data. Polynomial neural network for dependence of variables identification (D-PNN) describes a functional dependence of input variables (not entire patterns). It approximates a hyper-surface of this function with multi-parametric particular polynomials forming its functional output as a generalization of input patterns. This new type of neural network is based on GMDH polynomial neural network and was designed by author. D-PNN operates in a way closer to the brain learning as the ANN does. The ANN is in principle a simplified form of the PNN, where the combinations of input variables are missing.

A neural network application to assess magma diversity in the Etendeka igneous province, Namibia

2021 ◽  
Author(s):  
T.M. Owen-Smith ◽  
R.B. Trumbull ◽  
K. Bauer ◽  
J.K. Keiding ◽  
T.M. Will
Keyword(s):  
Neural Network ◽  
Equal Weight ◽  
Element Abundances ◽  
The Neural Network ◽  
Igneous Provinces ◽  
Alternative Approach ◽  
Wide Range ◽  
The Difference ◽  
Input Variables ◽  
Intrusive Suite

Abstract The geochemical discrimination of different magma types in Large Igneous Provinces is conventionally based on a few, pre-selected variables that are regarded to have petrological meaning. An alternative approach explored in this study is to apply the neural network technique of self-organising maps (SOM) to identify inherent groupings in data without knowledge or assumptions (unsupervised learning). The dataset used in this study comprises whole-rock analyses from extrusive (lava) and intrusive (dykes, sills) mafic suites in the Etendeka province, Namibia, taken from published sources and augmented by 103 new chemical analyses of dykes. Six SOM-classified groups are identified, which are unevenly distributed among the extrusive and the intrusive rock suites. The lava samples are dominated by just three of the six SOM groups (95% of all samples) and one group is absent entirely, whereas all six groups are present in the intrusive suite and five of them each comprise more than 5% of the samples. The geographic distribution of SOM-grouped dykes is heterogeneous and groups that are under-represented in the lava suite occur preferentially in a region of the pre-Etendeka basement where few lavas are preserved. Thus, the difference in magma diversity between intrusive and extrusive suites may be partly an artefact of erosion, which implies that a proper assessment of magma diversity in this and other LIPs must include the intrusive components. The correspondence of our SOM groupings with magma types in the Etendeka province that were established from petrologically defined variables is reasonably good for most trace-element abundances and ratios. However, some of the SOM groups have a wide range of initial Sr–Nd isotope ratios and a poor correspondence with the established magma types. We conclude that the SOM approach is useful for sorting out large and complex geochemical datasets but the method gives all input variables equal weight, which may be problematic if they have different responses to processes in the system under study (e.g., partial melting, fractional crystallisation, degassing, alteration). It is no substitute for expert petrological knowledge in discriminating genetically distinct magma types in an application like the present one.

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