Knot Optimization with Recursive Partitioning in Functional Data Analysis
(2021) STAN40 20211Department of Statistics
- Abstract
- Functional Data Analysis (FDA) is a field that has been growing rapidly over the last few decades, with much ongoing research and many recent publications. The focus for Functional Data Analysis is the study of so called functional data, that is data that is assumed to have been generated from a true, underlying function, where we can only observe a sequence of measurements.
We propose a method that can identify a suitable placement of knots purely based on the data, without any predefined basis functions.
For functional data specifically, some recent research has been published where the authors introduce tree based methods for knot placement. In this thesis we continue that research and investigate the method further by fully... (More) - Functional Data Analysis (FDA) is a field that has been growing rapidly over the last few decades, with much ongoing research and many recent publications. The focus for Functional Data Analysis is the study of so called functional data, that is data that is assumed to have been generated from a true, underlying function, where we can only observe a sequence of measurements.
We propose a method that can identify a suitable placement of knots purely based on the data, without any predefined basis functions.
For functional data specifically, some recent research has been published where the authors introduce tree based methods for knot placement. In this thesis we continue that research and investigate the method further by fully following the regression tree paradigm with evaluation of different methods to avoid over-fitting. Throughout this thesis we will call this method Knot Optimization with Recursive Partitioning (KORP).
We have evaluated our method on both simulated data sets and on the MNIST handwriting data set and compared both with uniform placement of knots and a genetic algorithm for identifying optimal placement of knots.
Our conclusion from the study of the proposed method, is that the method works very well, both for simple data sets and for functional data. It generally performs better than both Uniform placement and Genetic Algorithms. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9067637
- author
- Jönsson, Mattias LU and Kleverman, Marcus LU
- supervisor
- organization
- course
- STAN40 20211
- year
- 2021
- type
- H1 - Master's Degree (One Year)
- subject
- language
- English
- id
- 9067637
- date added to LUP
- 2023-02-14 11:25:28
- date last changed
- 2023-02-14 11:25:28
@misc{9067637,
abstract = {{Functional Data Analysis (FDA) is a field that has been growing rapidly over the last few decades, with much ongoing research and many recent publications. The focus for Functional Data Analysis is the study of so called functional data, that is data that is assumed to have been generated from a true, underlying function, where we can only observe a sequence of measurements.
We propose a method that can identify a suitable placement of knots purely based on the data, without any predefined basis functions.
For functional data specifically, some recent research has been published where the authors introduce tree based methods for knot placement. In this thesis we continue that research and investigate the method further by fully following the regression tree paradigm with evaluation of different methods to avoid over-fitting. Throughout this thesis we will call this method Knot Optimization with Recursive Partitioning (KORP).
We have evaluated our method on both simulated data sets and on the MNIST handwriting data set and compared both with uniform placement of knots and a genetic algorithm for identifying optimal placement of knots.
Our conclusion from the study of the proposed method, is that the method works very well, both for simple data sets and for functional data. It generally performs better than both Uniform placement and Genetic Algorithms.}},
author = {{Jönsson, Mattias and Kleverman, Marcus}},
language = {{eng}},
note = {{Student Paper}},
title = {{Knot Optimization with Recursive Partitioning in Functional Data Analysis}},
year = {{2021}},
}