A new tree-structured self-organizing map for data analysis

Abstract

Self-organizing map has been applied to a variety of tasks including data visualization and clustering. Once the point density of the neurons approximates the density of data, it is possible to miner clustering information from the data set after its unsupervised learning by using the neuron's relations. This paper presents a new algorithm for dynamical generation of a hierarchical structure of selforganizing maps with applications to data analysis. Di' erently from other tree-structured SOM approaches, which nodes are neurons, in this case the tree nodes are actually maps. From top to down, maps are automatically segmented by using the U-matrix information, which presents relations between neighboring neurons. The automatic map partitioning algorithm is based on mathematical morphology segmentation and it is applied to each map in each level of the hierarchy. Clusters of neurons are automatically identified and labeled and generate new sub-maps. Data are partitioned accordingly the label of its best match unit in each level of the tree. The algorithm may be seen as a recursive partition clustering method with multiple prototypes cluster representation, which enables the discoveries of clusters in a variety of geometrical shapes.

U-array: Extensão da U-matrix para Mapas Auto-Organizáveis com Espaço de Saída 3-D

“…As fórmulas para as outras distâncias são apresentadas nas equações 4-10. (9) A distância dxyz é uma média das distâncias entre os vértices opostos do cubo: …”

“…Este artigo apresenta o U-array como uma extensão da U-matrix para mapas com espaço de saída 3-D. A vantagem de se trabalhar com mapas com maiores espaços de saída é exatamente diminuir a interferência da redução da dimensionalidade nas distorções obtidas no processo automático de extração de classes do SOM. Como dispomos de métodos automáticos de extração de classes [1,[4][5][6][7][8][9] não há necessidade de visualização. U-arrays de dimensão qualquer poderiam ser aplicados.…”

Expanding Self-Organizing Map for data visualization and cluster analysis

“…Most of them focus on how to visualize neurons clearly and classify data [3,14,16]. Some work has concentrated on better topology preservation.…”

“…By incorporating the fuzzy concept into the SOM, the Fuzzy SOM [13] is able to handle vague and imprecise data, but it demands a high computational cost for the membership functions. The tree-structured SOM [3] can generate a tree of SOM dynamically, It can handle many difficult data sets but it spends almost twice longer than the SOM [2].…”

“…The regular grid can be used as a convenient visualization surface for showing different features of data such as the cluster tendencies of the data [8,12,16]. SOMs have been successfully applied in various engineering applications covering areas such as pattern recognition, full-text and image analysis, vector quantization, regression, financial data analysis, traveling salesman problem, and fault diagnosis [3,4,6,7,10,14,18].…”