Date:     Friday 22 October 2010  at 3pm
   Location: 6301 JCMB

Jochen Einbeck (University of Durham)

"Principal curves: A versatile tool for data compression and beyond"


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:

Dr Natalia Bochkina
Lecturer in Statistics

School of Mathematics
King’s Buildings
University of Edinburgh
Mayfield Road
Edinburgh, EH9 3JZ

Tel: 0131 650 8597

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