Response mixture models based on supervised components: clustering floristic taxa

Julien Gibaud (1) , Xavier Bry (1) , Catherine Trottier (1, 2) , Frédéric Mortier (3, 4) , Maxime Réjou-Méchain (5)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 UPVM - Université Paul-Valéry - Montpellier 3
3 UPR Forêts et Sociétés - Forêts et Sociétés
4 Cirad-ES - Département Environnements et Sociétés
5 UMR AMAP - Botanique et Modélisation de l'Architecture des Plantes et des Végétations

In this paper, we propose to cluster outcomes in order to identify groups predicted by specific explanatory components. A response matrix Y is assumed to depend on a set X of explanatory variables, and a set A of additional covariates. Variables in X are supposed many and redundant, which implies some dimension reduction and regularization. By contrast, A contains few selected variables which are forced into the regression model, as they demand no regularization. The matrix Y is assumed partitioned into G unknown groups of responses. We suppose that the outcomes in each group are predictable from an appropriate number of specific orthogonal supervised components of X. The classification is based on a mixture model of the responses. To estimate the model, we propose a criterion extending that of Supervised Component-based Generalized Linear Regression (SCGLR), a PLS-type method, and develop an algorithm combining those of SCGLR and EM estimation: response mixture SCGLR (rmSCGLR). This new methodology is tested on simulated data and then applied to a floristic ecology dataset.

Mots clés: EM algorithm; Response mixture; SCGLR; Supervised components; Taxa classification

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]

Julien Gibaud, Xavier Bry, Catherine Trottier, Frédéric Mortier, Maxime Réjou-Méchain. Response mixture models based on supervised components: clustering floristic taxa. 2022. ⟨hal-03547177v1⟩