An Autoencoder-like Non-Negative Matrix Factorization with Structure Regularization Algorithm for Clustering

Clustering plays a crucial role in data mining and knowledge discovery, where non-negative matrix factorization (NMF) has attracted widespread attention due to its effective data representation and dimensionality reduction capabilities. However, standard NMF has inherent limitations when processing sampled data embedded in low-dimensional manifold structures within high-dimensional ambient spaces, failing to effectively capture the complex structural information hidden in feature manifolds and sampling manifolds, and neglecting the learning of global structures. To address these issues, a novel structure regularization autoencoder-like non-negative matrix factorization for clustering (SRANMF) is proposed. Firstly, based on the non-negative symmetric encoder-decoder framework, we construct an autoencoder-like NMF model to enhance the characterization ability of latent information in data. Then, by fully considering high-order neighborhood relationships in the data, an optimal graph regularization strategy is introduced to preserve multi-order topological information structures. Additionally, principal component analysis (PCA) is employed to measure global data structures by maximizing the variance of projected data. Comparative experiments on 11 benchmark datasets demonstrate that SRANMF exhibits excellent clustering performance. Specifically, on the large-scale complex datasets MNIST and COIL100, the clustering evaluation metrics improved by an average of 35.31% and 46.17% (ACC) and 47.12% and 18.10% (NMI), respectively.