DDK

Data driven orthogonal basis selection for functional data analysis

This is an R implementation for the data driven orthogonal basis selection for functional data analysis paper. For more details see the arxiv link for the paper, Machine Learning Assisted Orthonormal Basis Selection for Functional Data Analysis.

In this work, we propose machine learning style techniques for the placement of the knots. The chosen knots are used to build orthogonal splines basis functions f_k(t), k = 1, ..., K that are used in basis function expansion to convert the data from discrete recorded data into a functional one. The method address the problem of the choice of the initial functional basis selection for functional data analysis.

DKK algorithm

For a more detailed description see the paper.

Input : knot search interval, θ - validation hyperparameter, 𝒳_train - training data, 𝒳_valid

• validation data - Find the first global knot ξ using equation on 𝒳_train.

• Add split to I at the location of ξ and add ξ to 𝒦⁽⁰⁾, the initial set of knots.

• Set s = 1.

While stopping condition (see the stopping condition in the paper) on 𝒳_valid is satisfied

1. Find the new optimal placement using equation ;
2. Add split to I at the location of the new selected knot ξ_s.
3. s = s + 1

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("ranibasna/ddk")

Reproducing the results in the paper

For reproducing the results presented in the paper for the Wine data, see this link