# [BAS17] Clusterwise analysis for multiblock component methods

**Revue Internationale avec comité de lecture : **
*Journal Advances in Data Analysis and Classification*,

vol. 12(2),

pp. 285-313,
2017, (

doi:

10.1007/s11634-017-0296-8)

**Mots clés: ** Multiblock component method. Clusterwise regression. Typological regression.
Cluster analysis. Dimension reduction.

**Résumé: **
Multiblock component methods are applied to data sets for which several blocks of
variables are measured on a same set of observations with the goal to analyse the relationships
between these blocks of variables. In this article, we focus on multiblock component methods
that integrate the information found in several blocks of explanatory variables in order to
describe and explain one set of dependent variables. In the following, multiblock PLS (MBPLS)
and multiblock redundancy analysis (MBRA) are chosen, as particular cases of multiblock
component methods when one set of variables is explained by a set of predictor variables that is
organized into blocks. Because these multiblock techniques assume that the observations come
from a homogeneous population they will provide suboptimal results when the observations
actually come from different populations. A strategy to palliate this problem—presented in this
article—is to use a technique such as clusterwise regression in order to identify homogeneous
clusters of observations. This approach creates two new methods that provide clusters that
have their own sets of regression coefficients. This combination of clustering and regression
improves the overall quality of the prediction and facilitates the interpretation. In addition,
the minimization of a well-defined criterion—by means of a sequential algorithm—ensures
that the algorithm converges monotonously. Finally, the proposed method is distribution-free
and can be used when the explanatory variables outnumber the observations within clusters.
The proposed clusterwise multiblock methods are illustrated with of a simulation study and a
(simulated) example from marketing.

Collaboration:
ANSES