A Comparison of Naive Bayes Classifiers with Applications to Self-Aware Aerospace Vehicles
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2017 American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Naive Bayes classifiers perform well on many problems, including problems that violate its simplistic assumptions. Several Naive Bayes classifiers are available in software packages, each differing in assumptions about the distribution of data. Despite acceptable performance, some accuracy is lost when assumptions are violated. For situations where the type, or shape, of the datas distribution may change with the system state, a Naive Bayes classifier that can handle more general distributions is desirable. In this paper, we derive two common Gaussian Naive Bayes classifiers, showing where assumptions are made about the datas distribution. Following this, an approximation to general Naive Bayes classifiers via partitioning is introduced as an alternative to specifying a parametric dis- tribution. The feature space is partitioned using a Voronoi decomposition, which provides an adaptive mesh as class density increases, and provides higher resolution in locally dense areas. We demonstrate that partitioning results in a classifier that is flexible to model assumptions and can approach the performance of a correctly derived Naive Bayes classifier, and we suggest a possible approach to better selection of partitions. This method requires little additional effort compared to deriving new Naive Bayes models to fit various modeling assumptions. Our methods are demonstrated on a medium altitude, long endurance aircraft.
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18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
