English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A new representation of splines that targets efficiency in the analysis offunctional data is implemented. The efficiency is achieved through two novelfeatures: using the recently introduced orthonormal spline bases, the so-called{\it splinets} and accounting for the spline support sets in the proposedspline object representation. The recently-introduced orthogonal splinets areevaluated by {\it dyadic orthogonalization} of the $B$-splines. The package isbuilt around the {\it Splinets}-object that represents a collection of splines.It treats splines as mathematical functions and contains information about thesupport sets and the values of the derivatives at the knots that uniquelydefine these functions. Algebra and calculus of splines utilize the Taylorexpansions at the knots within the support sets. Several orthonormalizationprocedures of the $B$-splines are implemented including the recommended dyadicmethod leading to the splinets. The method bases on a dyadic algorithm that canbe also viewed as the efficient method of diagonalizing a band matrix. Thelocality of the $B$-splines in terms of the support sets is, to a great extend,preserved in the corresponding splinet. This together with implementedalgorithms utilizing locality of the supports provides a valuable computationaltool for functional data analysis. The benefits are particularly evident whenthe sparsity in the data plays an important role. Various diagnostic tools areprovided allowing to maintain the stability of the computations. Finally, theprojection operation to the space of splines is implemented that facilitatesfunctional data analysis. An example of a simple functional analysis of thedata using the tools in the package is presented. The functionality of thepackage extends beyond the splines to piecewise polynomial functions, althoughthe splines are its focus.

Splinets -- splines through the Taylor expansion, their support sets and orthogonal bases