Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular and powerful method for dimensionality reduction. Despite its extensive use, there remains a need for a comprehensive analysis of NMF in the context of dimensionality reduction. To address this gap, this paper presents a comprehensive survey of NMF, focusing on its applications in both feature extraction and feature selection. We introduce a classification of dimensionality reduction, enhancing understanding of the underlying concepts. Subsequently, we delve into a thorough summary of diverse NMF approaches used for feature extraction and selection. Furthermore, we discuss the latest research trends and potential future directions of NMF in dimensionality reduction, aiming to highlight areas that need further exploration and development.

翻译：降维通过消除冗余特征、噪声及无关数据，在提升特征学习精度和减少训练时间方面起着关键作用。非负矩阵分解（NMF）已成为降维领域中广受欢迎且功能强大的方法。尽管其应用广泛，但关于NMF在降维中的全面分析仍显不足。为填补这一空白，本文对NMF进行了系统综述，重点关注其在特征提取和特征选择方面的应用。我们提出了一种降维分类方法，以加深对基本概念的理解。随后，我们深入总结了用于特征提取和特征选择的各类NMF方法。此外，本文讨论了NMF在降维中的最新研究趋势与潜在未来方向，旨在指出需进一步探索与发展的领域。