{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:37:52Z","timestamp":1760060272801,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Social Science Fund of China","award":["21BTJ042","23JRRA1186","2025QB-058"],"award-info":[{"award-number":["21BTJ042","23JRRA1186","2025QB-058"]}]},{"name":"Gansu Provincial Natural Science Foundation","award":["21BTJ042","23JRRA1186","2025QB-058"],"award-info":[{"award-number":["21BTJ042","23JRRA1186","2025QB-058"]}]},{"name":"Gansu Provincial Universities\u2019 Young Doctor Support Program","award":["21BTJ042","23JRRA1186","2025QB-058"],"award-info":[{"award-number":["21BTJ042","23JRRA1186","2025QB-058"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u201cdecoder-encoder\u201d 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.<\/jats:p>","DOI":"10.3390\/e27080875","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T13:08:51Z","timestamp":1755608931000},"page":"875","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Autoencoder-like Sparse Non-Negative Matrix Factorization with Structure Relationship Preservation"],"prefix":"10.3390","volume":"27","author":[{"given":"Ling","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5736-0600","authenticated-orcid":false,"given":"Haiyan","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"},{"name":"Key Laboratory of Digital Economy and Social Computing Science of Gansu, Lanzhou 730020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114105","DOI":"10.1016\/j.dss.2023.114105","article-title":"Predicting online customer purchase: The integration of customer characteristics and browsing patterns","volume":"177","author":"Kim","year":"2024","journal-title":"Decis. 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