By exploiting human insight in the form of a model, methods of composite hypothesis (CH) testing can generate more robust decision algorithms, with a greater ability to generalize, than the alternative “data-driven methods.” The latter include artificial neural networks, genetic algorithms, support vector machines, etc.
Within the field of CH testing an important class of models incorporates deterministic parameters, whose values are fixed but unknown, thereby precluding a Bayesian analysis. Among non-Bayesian methods, one dominated throughout the 20th century, the generalized likelihood ratio (GLR) test.
Now a new methodology has been developed for designing entire families of detectors to address every CH problem traditionally answered by a GLR test. This “continuum fusion” (CF) concept first generates the optimal detectors for all values of unknown parameters and then merges them, while imposing some choice of constraint on the process. The choice defines a fusion “flavor,” three of which have been investigated in detail.
The CF formalism comes with its own set of fundamental relations, partial differential equations and inequalities, whose solution define a given flavor. A fundamental theorem of CF has also been proven, showing that the GLR approach is always equivalent to a particular fusion flavor. The older test is thus dethroned, shown to be one of but many in a galaxy of non-Bayesian solutions to CH problems.
Several important models, which are especially appropriate to hyperspectral problems, can be solved in several CF flavors, without resorting to the equations. The models are described and then solved with purely geometrical arguments.
Dr. Alan Schaum received a Ph.D. in Theoretical Physics in 1978 from The Johns Hopkins University, where his research focused on relativistic quantum field theory. Until 1983 he applied queuing and information theories to network planning problems at Bell Laboratories in Holmdel, New Jersey. Since 1983 he has developed signal and image processing methods at The Naval Research Laboratory in Washington D.C., with an emphasis on multivariate detection theory and the modeling of hyperspectral signatures and their dynamics. Most recently he has developed a new theory of inference for addressing pattern recognition problems with model uncertainties.