Multiple Bayesian discriminant functions for high-dimensional massive data classification

The presence of complex distributions of samples concealed in high-dimensional, massive sample-size data challenges all of the current classification methods for data mining. Samples within a class usually do not uniformly fill a certain (sub)space but are individually concentrated in certain regions of diverse feature subspaces, revealing the class dispersion. Current classifiers applied to such complex data inherently suffer from either high complexity or weak classification ability, due to the imbalance between flexibility and generalization ability of the discriminant functions used by these classifiers. To address this concern, we propose a novel representation of discriminant functions in Bayesian inference, which allows multiple Bayesian decision boundaries per class, each in its individual subspace. For this purpose, we design a learning algorithm that incorporates the naive Bayes and feature weighting approaches into structural risk minimization to learn multiple Bayesian discriminant functions for each class, thus combining the simplicity and effectiveness of naive Bayes and the benefits of feature weighting in handling high-dimensional data. The proposed learning scheme affords a recursive algorithm for exploring class density distribution for Bayesian estimation, and an automated approach for selecting powerful discriminant functions while keeping the complexity of the classifier low. Experimental results on real-world data characterized by millions of samples and features demonstrate the promising performance of our approach.