# Noisy multi-label semi-supervised dimensionality reduction

## TL;DR

This paper introduces NMLSDR, a novel semi-supervised method for multi-label dimensionality reduction that denoises noisy labels and leverages unlabeled data to improve feature extraction in high-dimensional settings.

## Contribution

It proposes a new approach combining label denoising and semi-supervised learning for multi-label dimensionality reduction, addressing a gap in handling noisy labels in semi-supervised contexts.

## Key findings

- NMLSDR outperforms existing multi-label feature extraction methods.
- The method effectively denoises noisy multi-label data.
- Experimental results on synthetic, benchmark, and real-world data validate its superiority.

## Abstract

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.