Benchmarking multiblock methods with canonical factorization

Data measured on the same observations and organized in blocks of variables — from different measurement sources or deduced from topics specified by the user — are common in practice. Multiblock exploratory methods are useful tools to extract information from data in a reduced and interpretable common space. However, many methods have been proposed independently and the users are often lost in selecting the appropriate one, especially as they do not always lead to the same results or because outputs do not have the same form. For this purpose, the data decomposition by canonical factorization was introduced thus applied to some widely-used methods, CPCA, MCOA, MFA, STATIS and CCSWA. The methods were compared on simulated (resp. real) data whose structure is controlled (resp. known). Theoretical and practical results pinpoint that the block-structure must be carefully explored beforehand. The number of block-variables and the block-variance distribution along dimensions impacts the choice of the block-scaling. The observation-structure within and between blocks impacts the choice of the method. CPCA or MCOA mix common and specific information, STATIS highlights common structure only whereas CCSWA focuses on specific information. To enable these diagnoses, methods and proposed comparison tools are available on R, Matlab or Galaxy.