Abstract
Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want the segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l ∞ norm, and we present an optimal linear time algorithm based on a novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labelling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modelling.
AMS Subject Classification :
Notes
This is an expanded version of a conference paper Citation15.
The data is attributed to Ramsay and Silverman Citation16.