Cascaded dimensionality reduction nonnegative matrix factorization for data representation

Nonnegative matrix factorization (NMF), as a powerful dimensionality reduction technique, has attracted considerable attention for its excellent interpretability by utilizing relatively few linear combinations of basis vectors to represent the original data. The performance of its dimensionality reduction is affected by the quality and efficiency of finding a suitable collection of basis vectors. However, traditional NMF methods focus more on mining discriminative features rather than the quantity and quality of basis vectors. This may result in uncontrolled dimensionality and make it difficult to identify suitable basis vector sets, which can effectively capture the latent structure in the data. To alleviate these issues, we propose a cascaded dimensionality reduction nonnegative matrix factorization (CDRNMF) method. CDRNMF demonstrates distinctive attributes that differ from existing work as follows. (1) It subtly incorporates a feature selection mechanism into NMF, thereby establishing a novel cascaded dimensionality reduction framework that effectively retains the most representative features. (2) The dimensionality uncontrollability is effectively alleviated by constructing a feature selection matrix to assess and select basis vectors. (3) An optimization method is designed for solving CDRNMF efficiently. Numerical experiments validate that the performance of CDRNMF outperforms other state-of-the-art algorithms.