Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 장청재 | - |
dc.date.accessioned | 2022-08-05T06:07:10Z | - |
dc.date.available | 2022-08-05T06:07:10Z | - |
dc.date.issued | 2020-11 | - |
dc.identifier.citation | ADVANCES IN DATA ANALYSIS AND CLASSIFICATION, v. 15, no. 3, page. 673-699 | en_US |
dc.identifier.issn | 1862-5347 | - |
dc.identifier.issn | 1862-5355 | - |
dc.identifier.uri | https://link.springer.com/article/10.1007/s11634-020-00426-3 | - |
dc.identifier.uri | https://repository.hanyang.ac.kr/handle/20.500.11754/172163 | - |
dc.description.abstract | A growing number of problems in data analysis and classification involve data that are non-Euclidean. For such problems, a naive application of vector space analysis algorithms will produce results that depend on the choice of local coordinates used to parametrize the data. At the same time, many data analysis and classification problems eventually reduce to an optimization, in which the criteria being minimized can be interpreted as the distortion associated with a mapping between two curved spaces. Exploiting this distortion minimizing perspective, we first show that manifold learning problems involving non-Euclidean data can be naturally framed as seeking a mapping between two Riemannian manifolds that is closest to being an isometry. A family of coordinate-invariant first-order distortion measures is then proposed that measure the proximity of the mapping to an isometry, and applied to manifold learning for non-Euclidean data sets. Case studies ranging from synthetic data to human mass-shape data demonstrate the many performance advantages of our Riemannian distortion minimization framework. | en_US |
dc.description.sponsorship | Cheongjae Jang and Frank Chongwoo Park were supported in part by the NAVER LABS' AMBIDEX Project, MSIT-IITP (2019-0-01367, BabyMind), SNU-IAMD, SNU BK21+ Program in Mechanical Engineering, SNU Institute for Engineering Research, the National Research Foundation of Korea (NRF-2016R1A5A1938472), the Technology Innovation Program (ATC+, 20008547) funded by the Ministry of Trade, Industry, and Energy (MOTIE, Korea), and SNU BMRR Grant DAPAUD190018ID. Yung-Kyun Noh was supported by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT1901-13 and by Hanyang University (HY-2019). (Corresponding author: Frank Chongwoo Park.). | en_US |
dc.language.iso | en | en_US |
dc.publisher | SPRINGER HEIDELBERG | en_US |
dc.subject | Manifold learning | en_US |
dc.subject | Non-Euclidean data | en_US |
dc.subject | Riemannian geometry | en_US |
dc.subject | Distortion | en_US |
dc.subject | Harmonic map | en_US |
dc.title | A Riemannian geometric framework for manifold learning of non-Euclidean data | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1007/s11634-020-00426-3 | - |
dc.relation.page | 1-27 | - |
dc.relation.journal | ADVANCES IN DATA ANALYSIS AND CLASSIFICATION | - |
dc.contributor.googleauthor | Jang, Cheongjae | - |
dc.contributor.googleauthor | Noh, Yung-Kyun | - |
dc.contributor.googleauthor | Park, Frank Chongwoo | - |
dc.relation.code | 2020045428 | - |
dc.sector.campus | S | - |
dc.sector.daehak | RESEARCH INSTITUTE[S] | - |
dc.sector.department | INSTITUTION FOR ARTIFICIAL INTELLIGENCE RESEARCH HY_AIR | - |
dc.identifier.pid | cjjang | - |
dc.identifier.orcid | https://orcid.org/0000-0001-6029-4125 | - |
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