Bio-Inspired Prototype-Based Models and Applied Gompertzian Dynamics in Cluster Analysis

The thesis deals with the analysis of the clustering and mapping techniques derived from the principles of the neural and statistical learning and growth theory. The selected branch of the unsupervised bio-inspired prototype-based models is described in terms of the proposed logical framework, which highlights the continuity of these methods with the classical "pure" statistical methods. Moreover, as those methods are broadly understood as the "black boxes" with the unpredictable, unclear and especially hidden behavior, the examples of the spatial computational and organizational patterns in two-dimensional space are provided. Additionally, this thesis presents the novel concept based on the non-linear, non-Gaussian Gompertzian function, which has been widely used as the universal law in dynamic growth models, but has not yet been applied in the field of computational intelligence. The essence of Gompertzian dynamics is mathematically analyzed and a novel simple version of the Gompertzian normalized function is introduced. Furthermore, the function was modified for use in the field of artificial intelligence and neural implications were discussed. Additionally, the novel neural networks were proposed and derived from the topological principles of Kohonen's self-organizing maps and neural gas algorithm. The Gompertzian networks were evaluated using several indicators for various generated and real datasets. Gompertzian neural networks with fixed grid and integrated neighborhood ranking principle generally show lower mean squared errors than the original SOM algorithms. Likewise, the unconstrained Gompertzian networks have demonstrated overall low error rates comparable to neural gas algorithm, more stable and lower error solutions than the k- means sequential procedure. In conclusion, the Gompertzian function has been shown to be a viable concept and an effective computational tool for multidimensional data analysis.