{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T15:04:02Z","timestamp":1776265442353,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:00:00Z","timestamp":1776211200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>DBSCAN is widely used to identify structured regions in unlabeled data, but its performance depends critically on the selection of the neighborhood parameter \u03b5. Traditional heuristics for estimating \u03b5 often become unreliable in high-dimensional or varying-density settings because they rely heavily on local geometric criteria and may fail under smooth transitions or topological ambiguity. This work presents a three-level perspective on DBSCAN hyperparameter selection. At the algorithmic level, \u03b5 controls neighborhood connectivity and structural transitions in clustering. At the modeling level, the ordered k-distance signal is approximated through a surrogate dynamical estimation framework inspired by a mass\u2013spring\u2013damper system. At the causal level, the resulting estimator is interpreted through interventions on its internal threshold-selection mechanism. The proposed method models the variation of \u03b5 using ordinary differential equations defined on the ordered k-distance signal, enabling analysis of structural transitions in density organization via a surrogate dynamical representation. System identification is performed using L-BFGS-B optimization on the smoothed k-distance curve, while the system dynamics are solved with the fourth-order Runge\u2013Kutta method. The resulting estimator identifies transition regions that are structurally informative for \u03b5 selection in DBSCAN. To analyze the estimator at the intervention level, Pearl\u2019s do-calculus is used to compute the Average Causal Effect (ACE). The method was evaluated on synthetic benchmarks and on the Covtype dataset, including scenarios with multi-density overlap and dimensionality up to R10. The resulting ACE values, +0.9352, +0.5148, and +0.9246, indicate that the proposed estimator improves intervention-based \u03b5 selection relative to the geometric baseline across the evaluated datasets. Its practical computational cost is dominated by nearest-neighbor search, behaving approximately as O(NlogN) under favorable indexing conditions and degrading toward O(N2) in high-dimensional or weak-pruning regimes.<\/jats:p>","DOI":"10.3390\/e28040452","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T14:02:33Z","timestamp":1776261753000},"page":"452","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Causal Interpretation of DBSCAN Algorithm: A Dynamic Modeling for Epsilon Estimation"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-2169-1991","authenticated-orcid":false,"given":"K.","family":"Garcia-Sanchez","sequence":"first","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0444-9230","authenticated-orcid":false,"given":"J.-L.","family":"Perez-Ramos","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6635-5427","authenticated-orcid":false,"given":"S.","family":"Ramirez-Rosales","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7711-9585","authenticated-orcid":false,"given":"A.-M.","family":"Herrera-Navarro","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0827-6645","authenticated-orcid":false,"given":"H.","family":"Jim\u00e9nez-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6543-5078","authenticated-orcid":false,"given":"D.","family":"Canton-Enriquez","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Av. de las Ciencias S\/N, Juriquilla, Santiago de Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.ins.2022.11.139","article-title":"K-means clustering algorithms: A comprehensive review, variants analysis, and advances in the era of big data","volume":"622","author":"Ikotun","year":"2023","journal-title":"Inf. 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