{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:13Z","timestamp":1760145073398,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T00:00:00Z","timestamp":1718668800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62006102"],"award-info":[{"award-number":["62006102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the rapid advancements in data analysis and the increasing complexity of high-dimensional datasets, traditional dimensionality reduction techniques like Local Linear Embedding (LLE) often face challenges in maintaining accuracy and efficiency. This research aims to overcome the limitations of LLE, specifically its reliance on the nearest neighbor concept, its inability to distinguish differences among manifold points, and its underutilization of data discrimination information. To address these issues, we propose an advanced LLE algorithm that integrates decision tree-based neighbor recognition with Gaussian kernel density estimation. Decision trees accurately determine neighboring relationships, which are then optimized using Gaussian kernel density estimation to better reflect the distribution of sample points on the manifold. The algorithm also incorporates data discrimination information to enhance classification accuracy and efficiency. Evaluations in facial recognition tasks using SVM classifiers demonstrate significant improvements. Integrating decision trees (LLE-DT) yielded accuracy gains, with LFW at 98.75%, CFP 96.10%, and Olivetti 92.18%. Gaussian density estimation (LLE-GDE) achieved further enhancements, especially in LFW (99.13%), with CFP at 96.85%, and Olivetti at 91.82%. Combining both methods (LLE-DT-GDE) led to substantial improvements: LFW 99.61%, CFP 97.23%, and Olivetti 93.56%, highlighting the synergy between decision trees and Gaussian estimation. This advanced LLE algorithm effectively addresses the limitations of traditional approaches, showing promising results in complex data processing tasks such as facial recognition. These findings suggest its potential for broader applications in fields requiring robust data analysis and classification.<\/jats:p>","DOI":"10.3390\/sym16060765","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T05:27:19Z","timestamp":1718861239000},"page":"765","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Integration of Manifold Learning and Density Estimation for Fine-Tuned Face Recognition"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9175-5668","authenticated-orcid":false,"given":"Huilin","family":"Ge","sequence":"first","affiliation":[{"name":"School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyu","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiali","family":"Ouyang","sequence":"additional","affiliation":[{"name":"School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4085-8995","authenticated-orcid":false,"given":"Muhammad Awais","family":"Ashraf","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Chang\u2019an University, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiwen","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Umar Muhammad","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bellman, R. 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