Graph Regularization Methods in Soft Detector Fusion

Abstract

This paper presents a theoretical derivation of two new graph-based regularization methods for fusing the individual results of multiple detectors (two-class classifiers). The proposed approach considers linear combination of the individual detector statistics and its extension to a general nonlinear fusion method known as $\alpha $ -integration. A cost function that includes a mean-square error and a regularization term is minimized. The inclusion of the regularization term, which is based on graph signal processing, reduces the dispersion of the fused statistics, and thus improves the separation between the fused statistics corresponding to every detection hypothesis. The proposed methods (linear and non-linear regularized $\alpha $ -integration) are experimentally compared with commonly used classification methods (random forest, linear and quadratic discriminant analysis, and naive Bayes) and competitive fusion methods (Dempster-Shafer, copulas, behavior knowledge space, independent component analysis mixture modeling, majority voting, the mean, and $\alpha $ -integration). Two challenging problems were approached using simulated and electroencephalographic data, respectively: (i) detection of ultrasound pulses buried in high noise, and (ii) detection of changes in electroencephalographic signals for neuropsychological test staging. An experimental convergence analysis of the proposed regularized method for these two applications is included. Besides, the proposed methods were tested using several benchmark datasets. Results on the basis of classification accuracy, kappa index, F1 score, and receiver operating characteristic curve analysis demonstrate the superiority of the proposed regularized fusion methods.

Keywords

• Graph regularization
• detector fusion
• alpha integration
• graph signal processing
• electroencephalographic signal processing
• ultrasounds