Ordered Hypothesis Machines

Authors:
G. Beate Zimmer;Don Hush;Reid Porter
Affiliations:
Department of Mathematics and Statistics, Texas A&M University-Corpus Christi, Corpus Christi, USA;Los Alamos National Lab, Los Alamos, USA;Los Alamos National Lab, Los Alamos, USA
Venue:
Journal of Mathematical Imaging and Vision
Year:
2012

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Abstract

Stack Filters are a class of non-linear filter typically used for noise suppression. Advantages of Stack Filters are their generality and the existence of efficient optimization algorithms under mean absolute error (Wendt et al. in IEEE Trans. Acoust. Speech Signal Process. 34:898---910, 1986). In this paper we describe our recent efforts to use the class of Stack Filters for classification problems. This leads to a novel class of continuous domain classifiers which we call Ordered Hypothesis Machines (OHM). We develop convex optimization based learning algorithms for Ordered Hypothesis Machines and highlight their relationship to Support Vector Machines and Nearest Neighbor classifiers. We report on the performance on synthetic and real-world datasets including an application to change detection in remote sensing imagery. We conclude that OHM provides a novel way to reduce the number of exemplars used in Nearest Neighbor classifiers and achieves competitive performance to the more computationally expensive K-Nearest Neighbor method.