Heat Kernel Analysis of Syntactic Structures
We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin–Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood infor...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/132954 |
| _version_ | 1826202809734791168 |
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| author | Ortegaray, Andrew Berwick, Robert C. Marcolli, Matilde |
| author2 | Massachusetts Institute of Technology. Institute for Data, Systems, and Society |
| author_facet | Massachusetts Institute of Technology. Institute for Data, Systems, and Society Ortegaray, Andrew Berwick, Robert C. Marcolli, Matilde |
| author_sort | Ortegaray, Andrew |
| collection | MIT |
| description | We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin–Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood information. We analyze the different connectivity and clustering structures that arise in the two datasets, and the regions of maximal variance in the two-parameter space of the Belkin–Niyogi construction, which identify preferable choices of independent variables. We compute clustering coefficients and their variance. |
| first_indexed | 2024-09-23T12:19:38Z |
| format | Article |
| id | mit-1721.1/132954 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:19:38Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1329542024-06-04T20:06:51Z Heat Kernel Analysis of Syntactic Structures Ortegaray, Andrew Berwick, Robert C. Marcolli, Matilde Massachusetts Institute of Technology. Institute for Data, Systems, and Society We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin–Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood information. We analyze the different connectivity and clustering structures that arise in the two datasets, and the regions of maximal variance in the two-parameter space of the Belkin–Niyogi construction, which identify preferable choices of independent variables. We compute clustering coefficients and their variance. 2021-10-13T18:17:55Z 2021-10-13T18:17:55Z 2021-02 2020-12 2021-10-09T03:17:33Z Article http://purl.org/eprint/type/JournalArticle 1661-8270 1661-8289 https://hdl.handle.net/1721.1/132954 Ortegaray, A., Berwick, R.C. & Marcolli, M. Heat Kernel Analysis of Syntactic Structures. Math.Comput.Sci. 15, 643–660 (2021) en https://doi.org/10.1007/s11786-021-00498-0 Mathematics in Computer Science Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Ortegaray, Andrew Berwick, Robert C. Marcolli, Matilde Heat Kernel Analysis of Syntactic Structures |
| title | Heat Kernel Analysis of Syntactic Structures |
| title_full | Heat Kernel Analysis of Syntactic Structures |
| title_fullStr | Heat Kernel Analysis of Syntactic Structures |
| title_full_unstemmed | Heat Kernel Analysis of Syntactic Structures |
| title_short | Heat Kernel Analysis of Syntactic Structures |
| title_sort | heat kernel analysis of syntactic structures |
| url | https://hdl.handle.net/1721.1/132954 |
| work_keys_str_mv | AT ortegarayandrew heatkernelanalysisofsyntacticstructures AT berwickrobertc heatkernelanalysisofsyntacticstructures AT marcollimatilde heatkernelanalysisofsyntacticstructures |