{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T22:42:16Z","timestamp":1776811336199,"version":"3.51.2"},"reference-count":22,"publisher":"European Society of Computational Methods in Sciences and Engineering","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"published-print":{"date-parts":[[2021,1,19]]},"abstract":"<jats:p>1) The problem this paper is going to solve is how to determine the optimal number of dimension when using dimensionality reduction methods, and in this paper, we mainly use local linear embedding (LLE) method as example. 2) The solution proposed is on the condition of the parameter k in LLE is set in advance. Firstly, we select the parameter k, and compute the distance matrix of each feature in the source data and in the data after dimensionality reduction. Then, we use the Log-Euclidean metric to compute the divergence of the distance matrix between the features in the original data and in the low-dimensional data. Finally, the optimal low dimension is determined by the minimum Log-Euclidean metric. 3) The performances are verified by a public dataset and a handwritten digit dataset experiments and the results show that the dimension found by the method is better than other dimension number when classifying the dataset.<\/jats:p>","DOI":"10.3233\/jcm-204198","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T13:36:08Z","timestamp":1586871368000},"page":"1163-1173","source":"Crossref","is-referenced-by-count":3,"title":["Finding the optimal number of low dimension with locally linear embedding algorithm"],"prefix":"10.66113","volume":"20","author":[{"given":"Tao","family":"Yang","sequence":"first","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"}]},{"given":"Dongmei","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"}]},{"given":"Jintao","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"}]},{"given":"Jiqing","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China"}]},{"given":"Radim","family":"Burget","sequence":"additional","affiliation":[{"name":"Department of Telecommunication, Brno University of Technology, Czech"}]}],"member":"55691","reference":[{"key":"10.3233\/JCM-204198_ref1","first-page":"697","article-title":"Intrinsic dimension estimation using packing numbers","author":"K\u00e9gl","year":"2003","journal-title":"Advances in Neural Information Processing Systems"},{"key":"10.3233\/JCM-204198_ref2","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1038\/nn.3776","article-title":"Dimensionality reduction for large-scale neural recordings","volume":"17","author":"Cunningham","year":"2014","journal-title":"Nature Neuroscience"},{"key":"10.3233\/JCM-204198_ref3","first-page":"2859","article-title":"Linear dimensionality reduction: Survey, insights, and generalizations","volume":"16","author":"Cunningham","year":"2015","journal-title":"Journal of Machine Learning Research"},{"key":"10.3233\/JCM-204198_ref4","first-page":"174","article-title":"Symmetric kernel principal component analysis and its application in face recognition","volume":"39","author":"Zhenxue","year":"2013","journal-title":"Computer Engineering"},{"key":"10.3233\/JCM-204198_ref5","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.neucom.2015.03.116","article-title":"Manifold learning in local tangent space via extreme learning machine","volume":"174","author":"Wang","year":"2016","journal-title":"Neurocomputing"},{"key":"10.3233\/JCM-204198_ref6","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear dimensionality reduction by locally linear embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"10.3233\/JCM-204198_ref7","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.engappai.2015.12.010","article-title":"Incremental supervised locally linear embedding for machinery fault diagnosis","volume":"50","author":"Liu","year":"2016","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10.3233\/JCM-204198_ref8","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1016\/j.acha.2015.10.004","article-title":"A fast algorithm for manifold learning by posing it as a symmetric diagonally dominant linear system","volume":"40","author":"Vepakomma","year":"2016","journal-title":"Applied and Computational Harmonic Analysis"},{"key":"10.3233\/JCM-204198_ref9","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.ins.2016.01.069","article-title":"Efficient isometric multi-manifold learning based on the self-organizing method","volume":"345","author":"Fan","year":"2016","journal-title":"Information Sciences"},{"key":"10.3233\/JCM-204198_ref10","doi-asserted-by":"crossref","unstructured":"G. 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