Title: Partitionned matrices in multiset and multiway data analysis
Authors: Mohamed Hanafi - ONIRIS (France)
David Legland - INRA (France)
Pasquale Dolce - ONIRIS-Nantes (France) [presenting]
Abstract: It is well known that matrix algebra contributes to consolidate the mathematical basis of the multiset and multiway data methods, as well as to provide computational and geometric tools for the implementation of dedicated software. However, matrices and tensors do not cover the full range of data acquired in multiset and multiway data analysis. Indeed, the continuous development of sensors allows to acquire various kinds of measurement on one or more groups of individuals. Mathematically, these data can be conceptualized as partitioned matrices. Both matrix algebra and tensor algebra appear inadequate to manipulate partitioned matrices. The manipulation of partitioned matrices as simple matrices, without considering the associated partition, is inappropriate when the partition is an essential component of the problem to be solved, as for the so-called multiblock methods. Moreover, the partitioned matrices cannot be represented as tensors since the modes of blocks are all not identical. As a result, new specific rules for computation on partitioned matrices are needed. An appropriate vocabulary is introduced and discussed for partitioned matrices, standard notations for these entities and, in particular, different types of products between partitioned matrices. Furthermore, a computational kernel for handling partitioned matrices under R and Matlab environment will be presented.