Maximum A Posteriori EM MCE Logistic LASSO for learning fuzzy measures

A novel algorithm is introduced for learning fuzzy measures for Choquet integral-based information fusion. The new algorithm goes beyond previously published MCE-based approaches. It has the advantage that it is applicable to general measures, as opposed to only the Sugeno class of measures. In addition, the monotonicity constraints are handled easily with minimal time or storage requirements. Learning the fuzzy measure is framed as a maximum a posteriori (MAP) parameter learning problem. In order to maintain the constraints, this MAP problem is solved with a Gibbs sampler using an expectation maximization (EM) framework. For these reasons, the new algorithm is referred to as the MAP-EM MCE logistic LASSO algorithm. Results are given on synthetic and real data sets, the latter obtained from a landmine detection problem. Average reductions in false alarms of about 25% are achieved on the landmine detection problem and probabilities of detection in the interesting and meaningful range of 85%-95%.