[{"publication_status":"published","author":[{"full_name":"Pai, Gautam","last_name":"Pai","first_name":"Gautam"},{"orcid":"0000-0001-9699-8730","first_name":"Alexander","last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander"},{"full_name":"Talmon, Ronen","first_name":"Ronen","last_name":"Talmon"},{"first_name":"Ron","last_name":"Kimmel","full_name":"Kimmel, Ron"}],"scopus_import":"1","_id":"18225","type":"journal_article","article_number":"104461","OA_place":"publisher","fulldoi":"https://doi.org/10.1016/j.imavis.2022.104461","publisher":"Elsevier","title":"Deep isometric maps","abstract":[{"text":"Isometric feature mapping is an established time-honored algorithm in manifold learning and non-linear dimensionality reduction. Its prominence can be attributed to the output of a coherent global low-dimensional representation of data by preserving intrinsic distances. In order to enable an efficient and more applicable isometric feature mapping, a diverse set of sophisticated advancements have been proposed to the original algorithm to incorporate important factors like sparsity of computation, conformality, topological constraints and spectral geometry. However, a significant shortcoming of most approaches is the dependence on large-scale dense-spectral decompositions and the inability to generalize to points far away from the sampling of the manifold.\r\nIn this paper, we explore an unsupervised deep learning approach for computing distance-preserving maps for non-linear dimensionality reduction. We demonstrate that our framework is general enough to incorporate all previous advancements and show a significantly improved local and non-local generalization of the isometric mapping. Our approach involves training with only a few landmark points and avoids the need for population of dense matrices as well as computing their spectral decomposition.","lang":"eng"}],"article_type":"original","article_processing_charge":"No","month":"07","date_published":"2022-07-01T00:00:00Z","date_updated":"2024-10-14T11:03:26Z","oa":1,"quality_controlled":"1","day":"01","doi":"10.1016/j.imavis.2022.104461","volume":123,"oa_version":"Published Version","date_created":"2024-10-08T12:54:22Z","main_file_link":[{"url":"https://doi.org/10.1016/j.imavis.2022.104461","open_access":"1"}],"citation":{"ama":"Pai G, Bronstein AM, Talmon R, Kimmel R. Deep isometric maps. <i>Image and Vision Computing</i>. 2022;123. doi:<a href=\"https://doi.org/10.1016/j.imavis.2022.104461\">10.1016/j.imavis.2022.104461</a>","mla":"Pai, Gautam, et al. “Deep Isometric Maps.” <i>Image and Vision Computing</i>, vol. 123, 104461, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.imavis.2022.104461\">10.1016/j.imavis.2022.104461</a>.","apa":"Pai, G., Bronstein, A. M., Talmon, R., &#38; Kimmel, R. (2022). Deep isometric maps. <i>Image and Vision Computing</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.imavis.2022.104461\">https://doi.org/10.1016/j.imavis.2022.104461</a>","chicago":"Pai, Gautam, Alex M. Bronstein, Ronen Talmon, and Ron Kimmel. “Deep Isometric Maps.” <i>Image and Vision Computing</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.imavis.2022.104461\">https://doi.org/10.1016/j.imavis.2022.104461</a>.","ista":"Pai G, Bronstein AM, Talmon R, Kimmel R. 2022. Deep isometric maps. Image and Vision Computing. 123, 104461.","ieee":"G. Pai, A. M. Bronstein, R. Talmon, and R. Kimmel, “Deep isometric maps,” <i>Image and Vision Computing</i>, vol. 123. Elsevier, 2022.","short":"G. Pai, A.M. Bronstein, R. Talmon, R. Kimmel, Image and Vision Computing 123 (2022)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Image and Vision Computing","year":"2022","extern":"1","status":"public","publication_identifier":{"issn":["0262-8856"]},"intvolume":"       123","language":[{"iso":"eng"}]}]