ruth@utstat.uucp (Ruth Croxford) (09/27/88)
Topic: Principal Curves
Speaker: Trevor Hastie
Statistics and Data Analysis Group
AT&T Bell Laboratories
Murray Hill, New Jersey
Date: Thursday, September 29, 1988, 4:00 p.m.
Place: Sidney Smith Hall, room 2110, 100 St George St, University of Toronto
Abstract:
The first linear principal component of a p-dimensional point cloud provides
the line that minimizes the distance from the points to itself. It is a one
dimensional summary of the data, but often a linear summary is inadequate.
Principal curves are smooth one dimensional curves that pass through the middle
of the data. They minimize the distance from the points, a non-linear summary
of the data. In practice the curves are estimated using smoothers and so
their shape is suggested by the data.
After a brief introduction, I will show a short movie that illustrates
the curves and demonstrates an algorithm for fitting them. This will be
followed by some technical definitions and results. Finally, I will
briefly describe several areas of practical importance where the techniques
have been successfully applied.
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Coffee and tea will be served in the Delury Lounge (SS6006) at 3:30 p.m.