Multi-label classification extends the standard multi-class classification paradigm by dropping the assumption that classes have to be mutually exclusive, i.e., the same data item might belong to more than one class. Multi-label classification has many important applications in e.g. signal processing, medicine, biology and information security, but the analysis and understanding of the inference methods based on data with multiple labels are still underdeveloped. In this paper, we formulate a general generative process for multi-label data, i.e. we associate each label (or class) with a source. To generate multi-label data items, the emissions of all sources in the label set are combined. In the training phase, only the probability distributions of these (single label) sources need to be learned. Inference on multi-label data requires solving an inverse problem, models of the data generation process therefore require additional assumptions to guarantee well-posedness of the inference procedure. Similarly, in the prediction (test) phase, the distributions of all single-label sources in the label set are combined using the combination function to determine the probability of a label set. We formally describe several previously presented inference methods and introduce a novel, general-purpose approach, where the combination function is determined based on the data and/or on a priori knowledge of the data generation mechanism. This framework includes cross-training and new source training (also named label power set method) as special cases. We derive an asymptotic theory for estimators based on multi-label data and investigate the consistency and efficiency of estimators obtained by several state-of-the-art inference techniques. Several experiments confirm these findings and emphasize the importance of a sufficiently complex generative model for real-world applications.

Role mining algorithms address an important access control problem: configuring a role-based access control system. Given a direct assignment of users to permissions, role mining discovers a set of roles together with an assignment of users to roles. The results should closely agree with the direct assignment. Moreover, the roles should be understandable from the business perspective in that they reflect functional roles within the enterprise. This requires hybrid role mining methods that work with both direct assignments and business information from the enterprise.

Conventional clustering methods typically assume that each data item belongs to a single cluster. This assumption does not hold in general. In order to overcome this limitation, we propose a generative method for clustering vectorial data, where each object can be assigned to multiple clusters. Using a deterministic annealing scheme, our method decomposes the observed data into the contributions of individual clusters and infers their parameters. Experiments on synthetic Boolean data show that our method achieves higher accuracy in the source parameter estimation and superior cluster stability compared to state-of-the-art approaches. We also apply our method to an important problem in computer security known as role mining. Experiments on real-world access control data show performance gains in generalization to new employees against other multi-assignment methods. In challenging situations with high noise levels, our approach maintains its good performance, while alternative state-of-the-art techniques lack robustness.