{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:20:31Z","timestamp":1760059231536,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T00:00:00Z","timestamp":1748822400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R&amp;D Program of China","doi-asserted-by":"publisher","award":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"],"award-info":[{"award-number":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China","award":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"],"award-info":[{"award-number":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"]}]},{"name":"Natural Science Foundation of Inner Mongolia Autonomous Region of China","award":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"],"award-info":[{"award-number":["2024YFA1016200","12271166","W2412023","32030063","2025QN01044"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Selecting input data points in the context of high-dimensional, nonlinear, and complex data in Riemannian space is challenging. While optimal experimental design theory is well-established in Euclidean space, its extension to Riemannian manifolds remains underexplored. Li and Del Castillo recently obtained new theoretical results on D-optimal and G-optimal designs on Riemannian manifolds. This paper follows their framework to investigate A-optimal designs on such manifolds. We prove an equivalence theorem for A-optimality under the manifold regularization model. Based on this result, a sequential algorithm for identifying A-optimal designs on manifold data is developed. Numerical studies using both synthetic and real datasets show the validity of the proposed method.<\/jats:p>","DOI":"10.3390\/axioms14060436","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T10:21:49Z","timestamp":1748859709000},"page":"436","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Equivalence Theorem and A Sequential Algorithm for A-Optimal Experimental Designs on Manifolds"],"prefix":"10.3390","volume":"14","author":[{"given":"Jingwen","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Theory and Application in Statistics and Data Science\u2014MOE, School of Statistics, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaping","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Theory and Application in Statistics and Data Science\u2014MOE, School of Statistics, East China Normal University, Shanghai 200062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.4153\/CJM-1960-030-4","article-title":"The Equivalence of Two Extremum Problems","volume":"12","author":"Kiefer","year":"1960","journal-title":"Can. 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