{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:52:55Z","timestamp":1760143975504,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T00:00:00Z","timestamp":1709769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003827","name":"National Research, Development and Innovation Office\u2014NKFIH Fund","doi-asserted-by":"publisher","award":["SNN-135643","RRF-2.3.1-21-2022-00006"],"award-info":[{"award-number":["SNN-135643","RRF-2.3.1-21-2022-00006"]}],"id":[{"id":"10.13039\/501100003827","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Laboratory for Health Security","award":["SNN-135643","RRF-2.3.1-21-2022-00006"],"award-info":[{"award-number":["SNN-135643","RRF-2.3.1-21-2022-00006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph.<\/jats:p>","DOI":"10.3390\/a17030112","type":"journal-article","created":{"date-parts":[[2024,3,7]],"date-time":"2024-03-07T08:59:37Z","timestamp":1709801977000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exploratory Data Analysis and Searching Cliques in Graphs"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1941-7688","authenticated-orcid":false,"given":"Andr\u00e1s","family":"Hubai","sequence":"first","affiliation":[{"name":"R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e1ndor","family":"Szab\u00f3","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of P\u00e9cs, 7622 P\u00e9cs, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3060-0296","authenticated-orcid":false,"given":"Bogd\u00e1n","family":"Zav\u00e1lnij","sequence":"additional","affiliation":[{"name":"R\u00e9nyi Institute of Mathematics, 1053 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,7]]},"reference":[{"key":"ref_1","unstructured":"(2012). NIST\/SEMATECH e-Handbook of Statistical Methods."},{"key":"ref_2","unstructured":"Tukey, J.W. (1977). Exploratory Data Analysis, Person."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1080\/00031305.1980.10482706","article-title":"We need both exploratory and confirmatory","volume":"34","author":"Tukey","year":"1980","journal-title":"Am. Stat."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/B978-0-444-59528-7.00003-X","article-title":"Exploratory data analysis","volume":"28","author":"Vigni","year":"2013","journal-title":"Data Handl. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Baillie, M., Le Cessie, S., Schmidt, C.O., Lusa, L., Huebner, M., and Topic Group \u201cInitial Data Analysis\u201d of the STRATOS Initiative (2022). Ten simple rules for initial data analysis. PLoS Comput. Biol., 18.","DOI":"10.1371\/journal.pcbi.1009819"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chatfield, C. (1995). Problem Solving: A Statistician\u2019s Guide, Chapman and Hall. [2nd ed.].","DOI":"10.1201\/b15238"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1146\/annurev-clinpsy-032813-153700","article-title":"Exploratory Structural Equation Modeling: An Integration of the Best Features of Exploratory and Confirmatory Factor Analysis","volume":"10","author":"Marsh","year":"2014","journal-title":"Annu. Rev. Clin. Psychol."},{"key":"ref_8","unstructured":"Laczk\u00f3, J., Boltzheim, L., Malik, S., Mravcsik, M., and Szab\u00f3, S. (2024, February 28). Graph Based Dimension Reduction to Discern Synergies in Cyclic Arm Movements. Available online: https:\/\/science-cloud.hu\/en\/publications\/graph-based-dimension-reduction-discern-kinematic-synergies-cycling-arm-movements."},{"key":"ref_9","unstructured":"Garey, M.R., and Johnson, D.S. (2003). Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TAC.1959.1104847","article-title":"On adaptive control processes","volume":"4","author":"Bellman","year":"1959","journal-title":"IRE Trans. Autom. Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v031.i07","article-title":"Computing and Visualizing Dynamic Time Warping Alignments in R: The dtw Package","volume":"31","author":"Giorgino","year":"2009","journal-title":"J. Stat. Softw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.artmed.2008.11.007","article-title":"Matching incomplete time series with dynamic time warping: An algorithm and an application to post-stroke rehabilitation","volume":"45","author":"Tormene","year":"2009","journal-title":"Artif. Intell. Med."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3355502","article-title":"Scalable Kernelization for Maximum Independent Sets","volume":"24","author":"Hespe","year":"2019","journal-title":"ACM J. Exp. Algorithm."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10732-017-9337-x","article-title":"Finding near-optimal independent sets at scale","volume":"23","author":"Lamm","year":"2017","journal-title":"J. Heuristics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF02294026","article-title":"The analytical solution of the additive constant problem","volume":"48","author":"Cailliez","year":"1983","journal-title":"Psychometrika"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cox, T.F., and Cox, M.A.A. (2001). Multidimensional Scaling, Chapman and Hall. [2nd ed.].","DOI":"10.1201\/9780367801700"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1093\/biomet\/53.3-4.325","article-title":"Some distance properties of latent root and vector methods used in multivariate analysis","volume":"53","author":"Gower","year":"1966","journal-title":"Biometrika"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/3\/112\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:10:28Z","timestamp":1760105428000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/3\/112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,7]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["a17030112"],"URL":"https:\/\/doi.org\/10.3390\/a17030112","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2024,3,7]]}}}