Aggregate outputs learning differs from the classical supervised learning setting in that, training samples are packed into bags with only the aggregate outputs (labels for classification or real values for regression) known. This setting of the problem is associated with several kinds of application background. We focus on the aggregate outputs classification problem in this paper, and set up a manifold regularization framework to deal with it. The framework can be of both instance level and bag level for different testing goals. We propose four concrete algorithms based on our framework, each of which can cope with both binary and multi-class scenarios. The experimental results on several datasets suggest that our algorithms outperform the stateof-art technique.

Inspired by the fact that the final decision rule is mainly affected by a small subset of the training samples, i.e., Support Vector Machine (SVM) shows that the decision function relies on the few samples that are on or over the margin. We propose a new framework that explicitly strengthen this intuitive fact by adding an l1-norm regularizer. We give different formulations for our framework in different scenarios, and the experiments show that our framework can not only lead to high sparse solutions but also better performance than traditional methods.