ACP relationnelle pour l'analyse du mouvement : application à la danse
Résumé
In this paper, we apply a variant of Principal Component Analysis (PCA) to data coming from classical dance movement observation. The movement capture is achieved by means of sensors conveniently fastened to the dancer's body, which provide a series of regular space positions during the choreographic figure performance. Since data are time dependant, we intend that their temporal order is taken into account by the analysis technique we apply. Consequently, we refer to 'Relational PCA', that is a generalisation of usual PCA, and is based upon an additional relational parameter called the 'Graph Laplacian'. The Graph Laplacian accounts for a time neighbourhood within the set of observations. The span of the neighbourhood can be set by the analyst in order to control which pairs of observations will effectively contribute to sensors covariance. As an application, we propose the analysis of three typical classical dance movements, e.g. : 'Bending, Fall', 'Turn Jumped' and 'Walk'. With the first movement we show an instance of the analysis technique ; with the second, we discuss movement reconstruction through selected principal components, and with the last one, we give a criterion and way for choosing an optimal span for the Graph Laplacian.