Fuzzy partitions: a way to integrate expert knowledge into distance calculations

Serge Guillaume (1) , Brigitte Charnomordic (2) , Patrice Loisel (2)

1 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

This work proposes a new pseudo-metric based on fuzzy partitions (FPs). This pseudo-metric allows for the introduction of expert knowledge into distance computations performed on numerical data and can be used in various types of statistical clustering or other applications. The knowledge is formalized by a FP, in which each fuzzy set represents a linguistic concept. The pseudo-metric is designed to respect the FP semantics. The univariate case is first studied, and the pseudo-metric behavior is discussed using synthetic experiments. Then, a multivariate version is proposed as a Minkowski-like combination of univariate distances or semi-distances. The value of the proposal is illustrated with two real-world case studies in the fields of Biology and Precision Agriculture.

Mots clés: SYSTEME EXPERT; SEGMENTATION; INFORMATIQUE; CONNAISSANCE EXPERTE; SEMI-SUPERVISED; METRIC; EXPERT KNOWLEDGE; CLUSTERING

Domaines: Sciences de l'environnement

Serge Guillaume, Brigitte Charnomordic, Patrice Loisel. Fuzzy partitions: a way to integrate expert knowledge into distance calculations. Information Sciences, 2013, 245, p. 76 - p. 95. ⟨10.1016/j.ins.2012.07.045⟩. ⟨hal-00857362⟩