Constrained matrix factorization for semi-weakly learning with label proportions

Abstract

Learning with label proportions (LLP) is a weakly supervised learning problem that is conceivable in many real-world applications, where the training data is given in bags of instances, and only knowing the proportions of data points belonging to a particular category for each bag. However, how to effectively address the LLP problem with high dimensional data and some labeled samples is still a challenging problem. In this paper, we firstly propose a novel learning problem called semi-weakly learning with label proportions (SLLP), which has more extensive application scenarios. Then, we contribute a novel method based on non-negative matrix factorization, called Proportion Constrained Matrix Factorization (PCMF). It can not only effectively incorporate the label and proportion information, but also explore the local manifold structure information of training data. Moreover, the proposed method can make the data points from the same class be more likely merged together in the latent representation space, which leads to the more discriminating power. Sufficient experimental results on the benchmark datasets demonstrates its superiority over the state-of-the-art methods for LLP problem and efficiency on solving the SLLP problem.