Alpha integration methods have been used for integrating stochastic models and fusion in the context of detection (binary classification). Our work proposes separated score integration (SSI), a new method based on alpha integration to perform soft fusion of scores in multiclass classification problems, one of the most common problems in automatic classification. Theoretical derivation is presented to optimize the parameters of this method to achieve the least mean squared error (LMSE) or the minimum probability of error (MPE). The proposed alpha integration method was tested on several sets of simulated and real data. The first set of experiments used synthetic data to replicate a problem of automatic detection and classification of three types of ultrasonic pulses buried in noise (four-class classification). The second set of experiments analyzed two databases (one publicly available and one private) of real polysomnographic records from subjects with sleep disorders. These records were automatically staged in wake, rapid eye movement (REM) sleep, and non-REM sleep (three-class classification). Finally, the third set of experiments was performed on a publicly available database of single-channel real electroencephalographic data that included epileptic patients and healthy controls in five conditions (five-class classification). In all cases, alpha integration performed better than the considered single classifiers and classical fusion techniques.

We present a new method for fusing scores corresponding to different detectors (two-hypotheses case). It is based on alpha integration, which we have adapted to the detection context. Three optimization methods are presented: least mean square error, maximization of the area under the ROC curve, and minimization of the probability of error. Gradient algorithms are proposed for the three methods. Different experiments with simulated and real data are included. Simulated data consider the two-detector case to illustrate the factors influencing alpha integration and demonstrate the improvements obtained by score fusion with respect to individual detector performance. Two real data cases have been considered. In the first, multimodal biometric data have been processed. This case is representative of scenarios in which the probability of detection is to be maximized for a given probability of false alarm. The second case is the automatic analysis of electroencephalogram and electrocardiogram records with the aim of reproducing the medical expert detections of arousal during sleeping. This case is representative of scenarios in which probability of error is to be minimized. The general superior performance of alpha integration verifies the interest of optimizing the fusing parameters.