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• Alpha integration encompasses many classic fusion operators. • This paper proposes vector score integration (VSI), a new alpha integration method. • The parameters of VSI are optimized to achieve the minimum probability of error. • VSI was applied to two classification tasks using electroencephalographic signals. • VSI outperformed other fusion methods in both applications. Alpha integration is a family of integrators that encompasses many classic fusion operators (e.g., mean, product, minimum, maximum) as particular cases. This paper proposes vector score integration (VSI), a new alpha integration method for late fusion of multiple classifiers considering the joint effect of all the classes of the multi-class problem. Theoretical derivations to optimize the parameters of VSI for achieving the minimum probability of error are provided. VSI was applied to two classification tasks using electroencephalographic signals. The first task was the automatic stage classification of a neuropsychological test performed by epileptic subjects and the second one was the classification of sleep stages from apnea patients. Four single classifiers (linear and quadratic discriminant analysis, naive Bayes, and random forest) and three competitive fusion methods were estimated for comparison: mean, majority voting, and separated score integration (SSI). SSI is based on alpha integration, but unlike the proposed method, it considers the scores from each class in isolation, not accounting for possible dependencies among scores corresponding to different classes. VSI was able to optimally combine the results from all the single classifiers, in terms of accuracy and kappa coefficient, and outperformed the results of the other fusion methods in both applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]