Indices to Evaluate Self-Organizing Maps for Structures

Self-Organizing Maps for Structures (SOM-SD) are neural networks models capable of process- ing structured data, such as sequences and trees. The eval- uation of the encoding quality achieved by these maps can neither be measured exclusively by the quantization error as in the standard SOM, which fails to capture the struc- tural aspects, nor by indices measuring topology preserva- tion, because often there are no measures available for dis- crete structures. We propose new indices for the evaluation of encoding quality which are customized to the structural nature of input data. These indices are used to evaluate the quality of SOM-SDs trained on a benchmark dataset intro- duced earlier in [2]. We show that the proposed indices capture relevant structural features of the tree encoding ad- ditional to the statistical features of the training data vectors associated with the tree vertices.