Date of Award

2016

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Area of Concentration

Mathematics

Abstract

The ability to gather and store vast amounts of data at low cost has led to a number of challenges to those interested in searching for signal in said data; often there are legal and/or physical restrictions to storing the data at a single site. To work around such constraints requires new computational techniques. We explore a specific problemin, Independent Component Analysis, and offer a decentralized solution, ultimately setting a precedent for other kinds of interesting and dynamic collaborative analyses. We validate the method by application to temporal independent componant analysis for simulated and real functional magnetic resonance imaging (fMRI) data. Our results here indicate that the algorithm performs well on both sets of simulated and real fMRI data and what's more, as recent results indicate (Imitaz 2016), the method is amenable to privacy protection as measured by Dwork's differential privacy method.

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