Lynch, Brian
(2019)
Analysis of multi-way functional data under weak separability, with application to brain connectivity studies.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
This is the latest version of this item.
Abstract
We develop statistical methods for two-way functional data, in which we observe a sample of functions of two continuous variables, for example space and time. Analysis of two-way functional data presents complexities not found in traditional one-way functional data, and this analysis can serve as a starting point in understanding multi-way functional data. Motivated by the concept of factorizing the signal into separate spatial and temporal components, we develop the concept of weak separability of the underlying random process. Compared to the traditional strong separability assumption, which models the covariance structure as the product of the space and time covariances, weak separability is more flexible yet still interpretable, modeling the covariance structure as a weighted sum of strongly separable components.
We propose asymptotic and bootstrap testing procedures for weak separability, and their performance is studied in simulations. We apply the testing procedures to brain imaging data, in which functional connectivity between two brain regions is measured as a function of frequency and time. We illustrate how, under weak separability, the functional process can be understood in terms of products of basis functions for frequency and time. We go on to develop methods to approximate the covariance structure using L-separability, defined as a class of decompositions of the covariance structure under weak separability, and show its relationship to nonnegative matrix factorization. Using psychiatric data as a case study, we illustrate the L-separable decomposition, as well as two-way localization methods for the basis functions.
Share
| Citation/Export: |
|
| Social Networking: |
|
Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
30 January 2019 |
| Date Type: |
Publication |
| Defense Date: |
29 November 2018 |
| Approval Date: |
30 January 2019 |
| Submission Date: |
30 November 2018 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
124 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
asymptotics, functional principal component, hypothesis testing, marginal kernel, separable covariance, tensor product |
| Date Deposited: |
31 Jan 2019 00:02 |
| Last Modified: |
31 Jan 2019 00:02 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/35766 |
Available Versions of this Item
-
Analysis of multi-way functional data under weak separability, with application to brain connectivity studies. (deposited 31 Jan 2019 00:02)
[Currently Displayed]
Metrics
Monthly Views for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](/images/feed-icon-32x32.png){kind=icon}