Internship Project
Business and Economics

Principal component analysis of amplitude and phase variation for functional data taking values in a manifold

Institution
Humboldt-Universität zu Berlin
Chair of Statistics, School of Business and Economics
Subject Area
Statistics
Availability
Summer Term Internship 2023:
08 May – 28 July
 22 May – 11 August
 05 June – 25 August
 
Individual Timeframe Internship:
The dates are arranged individually according to the project's and the student's availability.
 
Internship Modality:
On-site internship in Berlin
Project Supervisor(s)
Prof. Dr. Sonja Greven
Academic Level
Advanced undergraduate students (from third year) 
Master's students 
Ph.D. students 
Language
English
Further Information
Project Type
Academic Research
Project Content
There are many manifold-valued functional data sets, especially trajectories on the earth’s surface, which suffer from phase variation. Some examples are the birds’ migration data analyzed in Su et al. (2014), in which they proposed a solution to the registration problem, and flight trajectories analyzed in Dai & Muller (2018), in which they offered PCA for manifold-valued functional data. The first two principal components of the flight trajectories, estimated by Dai & Muller (2018), visibly reflect the phase variation, which is ignored in the process of RFPCA in their work. Both datasets suffer from phase variation since each subject travels along trajectories with different speeds. This research project aims to provide the joint RFPCA of amplitude and phase variation to separate and identify the main patterns of variation in the shape of the trajectories and the speed of travelling along the trajectories.
Tasks for Interns
  • Statistical method development
  • Implementation in the statistical software R
  • Simulation studies
  • Application to at least one data set
  • Writing of a scientific report
Academic Level
Advanced undergraduate students (from third year) 
Master's students 
Ph.D. students 
Requirements
  • Good background in functional data analysis
  • Good mathematical and statistical background
  • R programming skills
  • Experience with applications and data analysis
Expected Preparation
  • Literature research on functional data, on manifolds, on functional principal component analysis, on phase and amplitude variation and registration approaches
  • Identification of suitable data sets for the application
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For more information on the Humboldt Internship Program or the project, please contact the program coordinator.