On the Impact of the Metrics Choice in SOM Learning: Some Empirical Results from Financial Data

Abstract

This paper studies the impact of the metrics choice on the learning procedure of Self Organizing Maps (SOM). In particular, we modified the learning procedure of SOM, by replacing the standard Euclidean norm, usually employed to evaluate the similarity between input patterns and nodes of the map, with the more general Minkowski norms: $||X||_p=\left(\displaystyle{\sum_{i}|X_i|^p}\right)^{\frac{1}{p}}$, for p ∈ ℝ₊. We have then analized how the clustering capabilities of SOM are modified when both prenorms (0 < p < 1), and ultrametrics (p > > 1) are considered. This was done using financial data on the Foreign Exchange Market (FOREX), observed at different time scales (from 1 minute to 1 month). The motivation inside the use of this data domain (financial data) is the relevance of the addressed question, since SOM are often employed to support the decision process of traders. It could be then of interest to know if and how the results of SOM can be driven by changes in the distance metric according to which proximities are evaluated. Our main result is that concentration seems not to be the unique factor affecting the effectiveness of the norms (and hence of the clustering procedure); in the case of financial data, the time scale of observations counts as well.