The linear ordered statistic (LOS) is a parameterized ordered statistic (OS) that is a weighted average of a rank-ordered sample. LOS operators are useful generalizations of aggregation as they can represent any linear aggregation, from minimum to maximum, including conventional aggregations, such as mean and median. In the fuzzy logic field, these aggregations are called ordered weighted averages (OWAs). Here, we present a method for learning LOS operators from training data, viz., data for which you know the output of the desired LOS. We then extend the learning process with regularization, such that a lower complexity or sparse LOS can be learned. Hence, we discuss what 'lower complexity' means in this context and how to represent that in the optimization procedure. Finally, we apply our learning methods to the well-known constant-false-alarm-rate (CFAR) detection problem, specifically for the case of background levels modeled by long-tailed distributions, such as the K-distribution. These backgrounds arise in several pertinent imaging problems, including the modeling of clutter in synthetic aperture radar and sonar (SAR and SAS) and in wireless communications.
Timothy C. Havens, Ian Cummings, Jonathan Botts, and Jason E. Summers, "Regularized learning of linear ordered-statistic constant false alarm rate filters (Conference Presentation)," Proc. SPIE 10186, Ocean Sensing and Monitoring IX, 101860V (Presented at SPIE Defense + Security: April 12, 2017; Published: 7 June 2017); https://doi.org/10.1117/12.2262614.5458109098001.
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