Gower-SOM: a self-organizing map for mixed data with gower distance and heuristic adaptation for data analytics
摘要
Self-organizing maps (SOMs) remain a benchmark technique for low-dimensional representation and cluster discovery; however, the original algorithm assumes Euclidean geometry and is therefore ill-suited to datasets that combine numerical, binary, and categorical features. This study introduces Gower-SOM, a topology-preserving neural network that replaces the Euclidean metric with Gower distance and incorporates probabilistic update rules for non-numeric features. The algorithm processes mixed-type data without one-hot-encoding or hierarchical transformations, thus avoiding dimensional inflation and semantic distortion. We evaluate Gower-SOM on three synthetic benchmarks designed to stress feature heterogeneity and on two publicly available datasets: Adult (approximately 48,000 instances, 14 features) and Obesity (approximately 2100 instances, 17 features). In comparison to the classical SOM, the proposed model reduces the normalized quantization error by 75–99% in synthetic scenarios and by 87% and 68% on the Adult and Obesity datasets, respectively. Cluster validity improves concurrently: the average silhouette index rises from 0.31 to 0.50 (adult) and from 0.43 to 0.48 (obesity), indicating minimal distortion of neighborhood relations. U-Matrix visualizations reveal sharper boundaries and more coherent attribute gradients, underscoring superior interpretability. These results demonstrate that Gower-SOM improves the mapping of mixed-type data without increasing algorithmic complexity, positioning it as a rigorous and scalable alternative for exploratory analysis, feature engineering, and decision support in domains where mixed-type data are the norm.