Supervised learning algorithms for multi-class classification problems with partial class memberships

In several application domains such as biology, computer vision, social network analysis and information retrieval, multi-class classification problems arise in which data instances not simply belong to one particular class, but exhibit a partial membership to several classes. Existing machine learning or fuzzy set approaches for representing this type of fuzzy information mainly focus on unsupervised methods. In contrast, we present in this article supervised learning algorithms for classification problems with partial class memberships, where class memberships instead of crisp class labels serve as input for fitting a model to the data. Using kernel logistic regression (KLR) as a baseline method, first a basic one-versus-all approach is proposed, by replacing the binary-coded label vectors with [0,1]-valued class memberships in the likelihood. Subsequently, we use this KLR extension as base classifier to construct one-versus-one decompositions, in which partial class memberships are transformed and estimated in a pairwise manner. Empirical results on synthetic data and a real-world application in bioinformatics confirm that our approach delivers promising results. The one-versus-all method yields the best computational efficiency, while the one-versus-one methods are preferred in terms of predictive performance, especially when the observed class memberships are heavily unbalanced.