Data driven orthogonal basis selection for functional data analysis

Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods, such as the principal component analysis, to so-represented data. While initial choice of a representation may have significant impact on second phase this issue has not gained much attention past. Typically, rather ad hoc some standard basis Fourier, wavelets, splines, etc. used for transforming purpose. To address important problem, we present its mathematical formulation, demonstrate importance, propose data-driven method observations. The chooses an by efficient placement knots. A simple machine learning style algorithm utilized knot selection recently introduced orthogonal spline bases - splinets are eventually taken represent benefits illustrated examples analyses sparse