Nikolay Nikolaev, Goldsmiths College, University of London

Summary of Research Interests

Research

The overall research themes of my scientific interests are theory and practice of the inductive computation. The inductive computation is an area in which there are addressed search problems by a variety of search paradigmss.

The last several years I have been working on stochastic search by genetic algorithms and genetic programming. This includes development of structured genetic algorithms with cooperative subpopulations [Slavov and Nikolaev, 1999c], and studies into their properties using NP-complete instances of the automata induction task [Slavov and Nikolaev, 1997a].

My preferred area is inductive genetic programming (IGP) [Nikolaev and Slavov, 1998d]. The research in this area investigated the fitness landscapes in IGP and their impact on search difficulties [Slavov and Nikolaev, 1997b], [Slavov and Nikolaev, 1998e]; the performance dynamics of evolutionary IGP search [Nikolaev and Slavov, 1998c]; the effect of different variable-size representations such as decision trees [Nikolaev and Slavov, 1997c, 1998a] and multivariate high-order polynomials [Nikolaev and Iba, 1999a] on the search behaviour.

I devoted my recent work to genetic programming of tree-structured polynomials, known as statistical learning networks of the GMDH type [Iba and Nikolaev, 2000a], [Nikolaev, and Iba, 2000b]. More precisely, this includes design of stochastic complexity (Minimum Description Length-MDL) [Nikolaev and Iba, 2000b], [Nikolaev and Iba, 1999a] and statistical [Iba and Nikolaev, 2000a] fitness functions for efficient search navigation. These functions are elaborated using ideas from the regularization theory aiming at evolution of parsimonious, accurate and predictive polynomials [Nikolaev and Iba, 2000b].

The goal of my research is to continue the improvement of the evolutionary IGP paradigm for successful applications in the fields of pattern recognition, classification, and system identification. I am currently working in several directions: 1) enhancing the tree-structured representations to utilize orthogonal polynomial, trigonometric functions, rational polynomials, NARMA polynomials, and dynamic recurrent polynomials; and 2) design of other statistical, algebraic, and information-theoretic fitness functions for IGP search guidance; 3) second-order backpropagation algorithms for re-training polynomial neural networks; 4) estimating confidence and prediction intervals of polynomial neural networks.

Successful results have been derived with sophisticated biocomputation systems, which are genetic algorithm and genetic programming systems made with immune network dynamics [Nikolaev, and Iba, 2001], [Slavov and Nikolaev, 1998b].

Some of my previous research on computational induction was devoted to machine learning and data mining with decision trees [Nikolaev and Slavov, 1997c].