Group method of data handling

Group method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models. Group method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models. GMDH is used in such fields as data mining, knowledge discovery, prediction, complex systems modeling, optimization and pattern recognition. Li et. al. (2017)'s results showed that GMDH neural network performed better than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network. GMDH algorithms are characterized by inductive procedure that performs sorting-out of gradually complicated polynomial models and selecting the best solution by means of the so-called external criterion. A GMDH model with multiple inputs and one output is a subset of components of the base function (1): where f are elementary functions dependent on different sets of inputs, a are coefficients and m is the number of the base function components. In order to find the best solution GMDH algorithms consider various component subsets of the base function (1) called partial models. Coefficients of these models are estimated by the least squares method. GMDH algorithms gradually increase the number of partial model components and find a model structure with optimal complexity indicated by the minimum value of an external criterion. This process is called self-organization of models. The most popular base function used in GMDH is the gradually complicated Kolmogorov-Gabor polynomial (2): The resulting models are also known as polynomial neural networks. Jürgen Schmidhuber cites GMDH as one of the earliest deep learning methods, remarking that it was used to train eight-layer neural nets as early as 1971. The method was originated in 1968 by Prof. Alexey G. Ivakhnenko in the Institute of Cybernetics in Kiev (then in the Ukrainian SSR).This approach from the very beginning was a computer-based method so, a set of computer programs and algorithms were the primary practical results achieved at the base of the new theoretical principles. Thanks to the author's policy of open code sharing the method was quickly settled in the large number of scientific laboratories worldwide. At that time code sharing was quite a physical action since the Internet is at least 5 years younger than GMDH. Despite this fact the first investigation of GMDH outside the Soviet Union had been made soon by R.Shankar in 1972. Later on different GMDH variants were published by Japanese and Polish scientists.