  Noisy labeled data represent a rich source of information that often are
easily accessible and cheap to obtain, but label noise might also have many
negative consequences if not accounted for. How to fully utilize noisy labels
has been studied extensively within the framework of standard supervised
machine learning over a period of several decades. However, very little
research has been conducted on solving the challenge posed by noisy labels in
non-standard settings. This includes situations where only a fraction of the
samples are labeled (semi-supervised) and each high-dimensional sample is
associated with multiple labels. In this work, we present a novel
semi-supervised and multi-label dimensionality reduction method that
effectively utilizes information from both noisy multi-labels and unlabeled
data. With the proposed Noisy multi-label semi-supervised dimensionality
reduction (NMLSDR) method, the noisy multi-labels are denoised and unlabeled
data are labeled simultaneously via a specially designed label propagation
algorithm. NMLSDR then learns a projection matrix for reducing the
dimensionality by maximizing the dependence between the enlarged and denoised
multi-label space and the features in the projected space. Extensive
experiments on synthetic data, benchmark datasets, as well as a real-world case
study, demonstrate the effectiveness of the proposed algorithm and show that it
outperforms state-of-the-art multi-label feature extraction algorithms.
