Interactive visualization and analysis of hierarchical neural projections for data mining

Dimensionality reducing mappings, often also denoted as multidimensional scaling, are the basis for multivariate data projection and visual analysis in data mining. Topology and distance preserving mapping techniques-e.g., Kohonen's self-organizing feature map (SOM) or Sammon's nonlinear mapping (NLM)-are available to achieve multivariate data projections for the following interactive visual analysis process. For large data bases, however, NLM computation becomes intractable. Also, if additional data points or data sets are to be included in the projection, a complete recomputation of the mapping is required. In general, a neural network could learn the mapping and serve for arbitrary additional data projection. However, the computational costs would also be high, and convergence is not easily achieved. In this work, a convenient hierarchical neural projection approach is introduced, where first an unsupervised neural network-e.g., a SOM-quantizes the data base, followed by fast NLM mapping of the quantized data. In the second stage of the hierarchy, an enhancement of the NLM by a recall algorithm is applied. The training and application of a second neural network, which is learning the mapping by function approximation, is quantitatively compared with this new approach. Efficient interactive visualization and analysis techniques, exploiting the achieved hierarchical neural projection for data mining, are presented.