Section: Research Program

Research axis 3: Functional data

Mainly due to technological advances, functional data are more and more widespread in many application domains. Functional data analysis (FDA) is concerned with the modeling of data, such as curves, shapes, images or a more complex mathematical object, though as smooth realizations of a stochastic process (an infinite dimensional data object valued in a space of eventually infinite dimension; space of squared integrable functions,...). Time series are an emblematic example even if it should not be limited to them (spectral data, spatial data,...). Basically, FDA considers that data correspond to realizations of stochastic processes, usually assumed to be in a metric, semi-metric, Hilbert or Banach space. One may consider, functional independent or dependent (in time or space) data objects of different types (qualitative, quantitative, ordinal, multivariate, time-dependent, spatial-dependent,...). The last decade saw a dynamic literature on parametric or non-parametric FDA approaches for different types of data and applications to various domains, such as principal component analysis, clustering, regression and prediction.