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Date: Friday 22 October 2010 at 3pm
Location: 6301 JCMB
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Jochen Einbeck (University of Durham)
"Principal curves: A versatile tool for data compression and beyond"
Abstract:
Principal curves were introduced about two decades ago as a
nonparametric generalization of linear principal component analysis.
Since then, they have been further developed and widely applied, for
example on the recognition of hand-written characters, the
reconstruction of river outlines or coastlines, and path estimation from
GPS tracks. A little bit surprisingly, most of the existing literature
seems to be happy with knowing that principal curves can be used for
descriptive applications of the type above, but has rarely proceeded
with exploiting the curve once it is there.
We focus in this talk on local principal curves (LPC), which are
constructed by iterating localized principal component steps. Using a
cubic spline representation, the curve can be fully parametrized,
enabling its use for tasks such as data compression, regression,
classification, or density estimation. This is illustrated using data
from the physical sciences. Further, some insight into theoretical
properties of LPCs is given, and the extension to local principal
surfaces or manifolds is briefly discussed.
Joint work with Ludger Evers (University of Glasgow)
Tea and coffee will be available after the seminar in the Mathematics
Common Room (5212).
The webpage for the seminar:
http://www.maths.ed.ac.uk/~nbochkin/StatisticsSeminar.html
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Dr Natalia Bochkina
Lecturer in Statistics
School of Mathematics
King’s Buildings
University of Edinburgh
Mayfield Road
Edinburgh, EH9 3JZ
Tel: 0131 650 8597
Email: [log in to unmask]
Webpage: http://www.maths.ed.ac.uk/~nbochkin/
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