Are your data gathered? The Folding Test of Unimodality

Alban Siffer (1, 2) , Pierre-Alain Fouque (1) , Alexandre Termier (3) , Christine Largouët (4, 3)

1 EMSEC - EMbedded SEcurity and Cryptography
2 AMOSSYS
3 LACODAM - Large Scale Collaborative Data Mining
4 AGROCAMPUS OUEST

Understanding data distributions is one of the most fundamental research topic in data analysis. The literature provides a great deal of powerful statistical learning algorithms to gain knowledge on the underlying distribution given multivariate observations. We are likely to find out a dependence between features, the appearance of clusters or the presence of outliers. Before such deep investigations , we propose the folding test of unimodality. As a simple statistical description, it allows to detect whether data are gathered or not (unimodal or multimodal). To the best of our knowledge, this is the first multivariate and purely statistical unimodality test. It makes no distribution assumption and relies only on a straightforward p−value. Through real world data experiments, we show its relevance and how it could be useful for clustering.

Mots clés: Multivariate statistics; CCS CONCEPTS • Mathematics of computing → Multivariate statistics; Non-parametric statistics; Exploratory data analysis; KEYWORDS Unimodality test

Domaines: Base de données [cs.DB]; Intelligence artificielle [cs.AI]; Statistiques [math.ST]

Alban Siffer, Pierre-Alain Fouque, Alexandre Termier, Christine Largouët. Are your data gathered? The Folding Test of Unimodality. KDD 2018 - 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Minin, Aug 2018, London, United Kingdom. pp.2210-2218, ⟨10.1145/3219819.3219994⟩. ⟨hal-01951676⟩