The self-organizing map (SOM) has been widely used as a software tool for visualization of high-dimensional data. Important SOM features include information compression while trying to preserve topological and metric relationship of the primary data items. Similar data in the input space would be mapped to the same neuron or in a nearby unit. The clustering properties of a trained SOM 2-D can be visualized by the U-matrix, which is a neuron's neighborhood distance based image. This assumption of topological preservation is not true for many SOM mappings involving dimension reduction. With the automation of cluster detection in SOM network higher output dimensions can be used in problems involving discovery of classes in multidimensional data. Results of topological errors are shown in a simple 2-D clustering in a 1-D output grid SOM. This paper presents the U-array as an extension of the U-matrix for 3-D output grids. The advantage of the method relies in working with higher dimensions in the output space, which can lead to a better topological preservation in data analysis. Examples of automatic class discovery using U-arrays are also presented.
Data Clustering; Volume Segmentation; Self-Organizing Maps; Neural Networks; Data Mining
