PHYSICS / MATHEMATICS DEPARTMENT SEMINAR
NEAR MINIMAX CONTINUOUS PIECEWISE LINEAR REPRESENTATIONS OF DISCRETE DATA
Dr. N. Brad Willms
Bishop's University
Friday, November 19, 2010
3:30 pm - 4:30 pm
Nicolls 315
An algorithm that constructs a continuous piecewise linear representation of a given set of discrete data, subject to a novel constraint relating the segments' slopes and lengths, is described. The constraint is determined by a user-specified parameter, tmin, which dictates the minimum length of segments whose slopes do not lie between the slopes of their neighbours. For reasonable tmin values, the resulting representation of the data captures the signal and both smooths the noise and provides a measure of it. The algorithm yields an optimal or near optimal representation, subject to this constraint, in the L8 norm and does so in at worst O(nK) time, where n is the number of data points and K the number of segments. The algorithm is described, its capabilities demonstrated with several examples, and potential applications are discussed.
