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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.