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.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-04-24T15:04:03Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) mapas-auto-organizaveis2.pdf: 2835656 bytes, checksum: 8836a86bd2cced9353cb25b53383b305 (MD5) / Made available in DSpace on 2017-04-24T15:04:03Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) mapas-auto-organizaveis2.pdf: 2835656 bytes, checksum: 8836a86bd2cced9353cb25b53383b305 (MD5) Previous issue date: 2016-08-16 / Métodos e algoritmos em aprendizado de máquina não supervisionado têm sido empregados em diversos problemas significativos. Uma explosão na disponibilidade de dados de várias fontes e modalidades está correlacionada com os avanços na obtenção, compressão, armazenamento, transferência e processamento de grandes quantidades de dados complexos com alta dimensionalidade, como imagens digitais, vídeos de vigilância e microarranjos de DNA. O agrupamento se torna difícil devido à crescente dispersão desses dados, bem como a dificuldade crescente em discriminar distâncias entre os pontos de dados. Este trabalho apresenta um algoritmo de agrupamento suave em subespaços baseado em um mapa auto-organizável (SOM) com estrutura variante no tempo, o que significa que o agrupamento dos dados pode ser alcançado sem qualquer conhecimento prévio, tais como o número de categorias ou a topologia dos padrões de entrada, nos quais ambos são determinados durante o processo de treinamento. O modelo também atribui diferentes pesos a diferentes dimensões, o que implica que cada dimensão contribui para o descobrimento dos aglomerados de dados. Para validar o modelo, diversos conjuntos de dados reais foram utilizados, considerando uma diversificada gama de contextos, tais como mineração de dados, expressão genética, agrupamento multivista e problemas de visão computacional. Os resultados são promissores e conseguem lidar com dados reais caracterizados pela alta dimensionalidade. / Unsupervised learning methods have been employed on many significant problems. A blast in the availability of data from multiple sources and modalities is correlated with advancements in how to obtain, compress, store, transfer, and process large amounts of complex high-dimensional data, such as digital images, surveillance videos, and DNA microarrays. Clustering becomes challenging due to the increasing sparsity of such data, as well as the increasing difficulty in discriminating distances between data points. This work presents a soft subspace clustering algorithm based on a self-organizing map (SOM) with time-variant structure, meaning that clustering data can be achieved without any prior knowledge such as the number of categories or input data topology, in which both are determined during the training process. The model also assigns different weights to different dimensions, this implies that every dimension contributes to uncover clusters. To validate the model, we used a number of real-world data sets, considering a diverse range of contexts such as data mining, gene expression, multi-view and computer vision problems. The promising results can handle real-world data characterized by high dimensionality.