Autoencoder-like Sparse Non-Negative Matrix Factorization with Structure Relationship Preservation

Clustering algorithms based on non-negative matrix factorization (NMF) have garnered significant attention in data mining due to their strong interpretability and computational simplicity. However, traditional NMF often struggles to effectively capture and preserve topological structure information between data during low-dimensional representation. Therefore, this paper proposes an autoencoder-like sparse non-negative matrix factorization with structure relationship preservation (ASNMF-SRP). Firstly, drawing on the principle of autoencoders, a "decoder-encoder" co-optimization matrix factorization framework is constructed to enhance the factorization stability and representation capability of the coefficient matrix. Then, a preference-adjusted random walk strategy is introduced to capture higher-order neighborhood relationships between samples, encoding multi-order topological structure information of the data through an optimal graph regularization term. Simultaneously, to mitigate the impact of noise and outliers, the l2,1-norm is used to constrain the feature correlation between low-dimensional representations and the original data, preserving feature relationships between data, and a sparse constraint is imposed on the coefficient matrix via the inner product. Finally, clustering experiments conducted on 8 public datasets demonstrate that ASNMF-SRP consistently exhibits favorable clustering performance.