Archetypal analysis is a mathematical procedure that describes a multivariate dataset by some underlying ideal types, the so-called archetypes. The aim is to find a few points (the archetypes), not necessarily observed, such that all the data points can be well approximated by convex combinations of them. At the same time, the archetypes must be a convex combination of the observed data. With this work, we extend this methodology to the case of functional data, i.e. to the analysis of curves or functions. We model each curve observed over time through a linear combination of basis functions. By mapping curves into the basis function coefficient space, we identify first archetypal coefficients, and then archetypal functions that describe some ideal patterns within complex functional data sets.
Archetypal Functions
PORZIO, Giovanni Camillo;
2012-01-01
Abstract
Archetypal analysis is a mathematical procedure that describes a multivariate dataset by some underlying ideal types, the so-called archetypes. The aim is to find a few points (the archetypes), not necessarily observed, such that all the data points can be well approximated by convex combinations of them. At the same time, the archetypes must be a convex combination of the observed data. With this work, we extend this methodology to the case of functional data, i.e. to the analysis of curves or functions. We model each curve observed over time through a linear combination of basis functions. By mapping curves into the basis function coefficient space, we identify first archetypal coefficients, and then archetypal functions that describe some ideal patterns within complex functional data sets.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
