Constrained matrix factorization for semi-weakly learning with label proportions

Highlights：

• We propose a novel learning problem called semi-weakly learning with label proportions (SLLP), which has more extensive application scenarios.

• We contribute a noval method based on non-negative matrix factorization, called Proportion Constrained Matrix Factorization (PCMF).

• This method can not only effectively incorporate the label and proportion information, but also explore the local manifold structure information of training data.

• It also 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.