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Knowl. Discov. Data"],"published-print":{"date-parts":[[2024,1,31]]},"abstract":"<jats:p>\n            Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this article, we propose\n            <jats:sc>Lap<\/jats:sc>\n            tSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically,\n            <jats:sc>Lap<\/jats:sc>\n            tSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding when learning to preserve the local and global structure from high-dimensional space to low-dimensional space. It is nontrivial to solve the proposed model because the eigenvalues of normalized symmetric Laplacian are functions of the decision variable. We provide a majorization-minimization algorithm with convergence guarantee to solve the optimization problem of\n            <jats:sc>Lap<\/jats:sc>\n            tSNE and show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective. We evaluate our method by a formal comparison with state-of-the-art methods on seven benchmark datasets, both visually and via established quantitative measurements. The results demonstrate the superiority of our method over baselines such as t-SNE and UMAP. We also provide out-of-sample extension, large-scale extension, and mini-batch extension for our\n            <jats:sc>Lap<\/jats:sc>\n            tSNE to facilitate dimensionality reduction in various scenarios.\n          <\/jats:p>","DOI":"10.1145\/3612932","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T12:04:16Z","timestamp":1691064256000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Laplacian-based Cluster-Contractive t-SNE for High-Dimensional Data Visualization"],"prefix":"10.1145","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3895-3280","authenticated-orcid":false,"given":"Yan","family":"Sun","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0517-8905","authenticated-orcid":false,"given":"Yi","family":"Han","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9665-0355","authenticated-orcid":false,"given":"Jicong","family":"Fan","sequence":"additional","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen and Shenzhen Research Institute of Big Data, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,9,6]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"1455","volume-title":"Proceedings of the 31st Conference On Learning Theory.","author":"Arora Sanjeev","year":"2018","unstructured":"Sanjeev Arora, Wei Hu, and Pravesh K. 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