Indices to Evaluate Self-Organizing Maps for Structures

Abstract

Self-Organizing Maps for Structures (SOM-SD) are neural networks models capable of processing structured data, such as sequences and trees. The evaluation of the encoding quality achieved by these maps should neither be measured only by the quantization error as in the standard SOM, which fails to capture the structural aspects, nor by other topology preserving indexes which are ill-defined for discrete structures. We propose new indexes for the evaluation of encoding quality which are customized to the structural nature of input data. These indexes are used to evaluate the quality of SOM-SDs trained on a benchmark dataset introduced earlier in. We show that the proposed indexes capture relevant structural features of the tree encoding additional to the statistical features of the training data labels.