The self-organizing map (SOM) is an unsupervised neural network which projects high-dimensional data onto a low-dimensional grid and visually reveals the topological order of the original data. Self-organizing maps have been successfully applied to many fields, including engineering and business domains. However, the conventional SOM training algorithm handles only numeric data. Categorical data are usually converted to a set of binary data before training of an SOM takes place. If a simple transformation scheme is adopted, the similarity information embedded between categorical values may be lost. Consequently, the trained SOM is unable to reflect the correct topological order. This paper proposes a generalized self-organizing map model that offers an intuitive method of specifying the similarity between categorical values via distance hierarchies and, hence, enables the direct process of categorical values during training. In fact, distance hierarchy unifies the distance computation of both numeric and categorical values. The unification is done by mapping the values to distance hierarchies and then measuring the distance in the hierarchies. Experiments on synthetic and real datasets were conducted, and the results demonstrated the effectiveness of the generalized SOM model.

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Clustering is an important function in data mining. Its typical application includes the analysis of consumer's materials. Adaptive resonance theory network (ART) is very popular in the unsupervised neural network. Type I adaptive resonance theory network (ART1) deals with the binary numerical data, whereas type II adaptive resonance theory network (ART2) deals with the general numerical data. Several information systems collect the mixing type attitudes, which included numeric attributes and categorical attributes. However, ART1 and ART2 do not deal with mixed data. If the categorical data attributes are transferred to the binary data format, the binary data do not reflect the similar degree. It influences the clustering quality. Therefore, this paper proposes a modified adaptive resonance theory network (M-ART) and the conceptual hierarchy tree to solve similar degrees of mixed data. This paper utilizes artificial simulation materials and collects a piece of actual data about the family income to do experiments. The results show that the M-ART algorithm can process the mixed data and has a great effect on clustering.

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