Abstract
In this paper, we propose a functional relative projection pursuit as an extended method of relative projection pursuit (Mizuta, 2002a) for functional data analysis. This method finds an 'interesting' structure of subset data in a low dimensional projection space of the functional data compared with the structure of the superset data. For example, it can detect some different part of functions such as a time cycle and amplitude between the subset functional data and the superset functional data. Projection pursuit (Friedman & Tukey, 1974) is one of the dimension reduction methods to search for an 'interesting' structure in low dimensional space. This method has been already extended for functional data analysis by Nason (1998), called functional projection pursuit. The both methods are powerful, but can only find the different structures from normal distribution, defined as an 'uninteresting' structure. We consider that 'interesting' structures are not always different from normal distribution because an 'interestingness' depends on factors such as purposes of an analysis. The aim of our method is to search for 'interesting' structures far from a distribution of a functional dataset as reference pre-defined by a user. We assess the effectiveness of our method compared with conventional projection pursuit using a numerical example. In addition, we introduce a case study, which is applied our method to the child development data of National study of health and growth (Holland et al., 1999a, b) in United Kingdom.
