{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T22:00:39Z","timestamp":1766181639406,"version":"3.37.3"},"reference-count":50,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100004410","name":"Scientific and Technological Research Council of Turkey","doi-asserted-by":"crossref","award":["2211-C"],"award-info":[{"award-number":["2211-C"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Info. Tech. Dec. Mak."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:p> Time series is a set of sequential data point in time order. The sizes and dimensions of the time series datasets are increasing day by day. Clustering is an unsupervised data mining technique that groups objects based on their similarities. It is used to analyze various datasets, such as finance, climate, and bioinformatics datasets. [Formula: see text]-means is one of the most used clustering algorithms. However, it is challenging to determine the value of [Formula: see text] parameter, which is the number of clusters. One of the most used methods to determine the number of clusters (such as [Formula: see text]) is cluster validity indexes. Several internal and external validity indexes are used to find suitable cluster numbers based on characteristics of datasets. In this study, we propose a hybrid validity index to determine the value of [Formula: see text] parameter of [Formula: see text]-means algorithm. The proposed hybrid validity index comprises four internal validity indexes, such as Dunn, Silhouette, C index, and Davies\u2013Bouldin indexes. The proposed method was applied to nine real-life finance and benchmarks time series datasets. The financial dataset was obtained from Yahoo Finance, consisting of daily closing data of stocks. The other eight benchmark datasets were obtained from UCR time series classification archive. Experimental results showed that the proposed hybrid validity index is promising for finding the suitable number of clusters with respect to the other indexes for clustering time-series datasets. <\/jats:p>","DOI":"10.1142\/s0219622021500449","type":"journal-article","created":{"date-parts":[[2021,6,29]],"date-time":"2021-06-29T02:01:16Z","timestamp":1624932076000},"page":"1615-1636","source":"Crossref","is-referenced-by-count":5,"title":["A Hybrid Validity Index to Determine K Parameter Value of k-Means Algorithm for Time Series Clustering"],"prefix":"10.1142","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1421-4670","authenticated-orcid":false,"given":"Fatma Ozge","family":"Ozkok","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Erciyes University, Kayseri, 38039, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mete","family":"Celik","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Erciyes University, Kayseri, 38039, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"S0219622021500449BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2020.113366"},{"key":"S0219622021500449BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.06.026"},{"key":"S0219622021500449BIB003","first-page":"91","volume-title":"International Symposium on Innovations in Intelligent Systems and Applications","author":"Celik M.","year":"2011"},{"key":"S0219622021500449BIB004","doi-asserted-by":"crossref","first-page":"840","DOI":"10.3906\/elk-1210-20","volume":"22","author":"Celik M.","year":"2014","journal-title":"Turkish Journal of Electrical Engineering & Computer Sciences"},{"issue":"6","key":"S0219622021500449BIB005","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1007\/s00284-018-1437-9","volume":"75","author":"Kesmen Z.","year":"2018","journal-title":"Current microbiology"},{"first-page":"504","volume-title":"7th International Conference on Advanced Technologies","author":"Celik M.","key":"S0219622021500449BIB006"},{"key":"S0219622021500449BIB007","doi-asserted-by":"publisher","DOI":"10.18201\/ijisae.2017533899"},{"volume-title":"7th International Conference on Advanced Technologies (ICAT\u201918)","year":"2018","author":"Ozekes A.","key":"S0219622021500449BIB008"},{"key":"S0219622021500449BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.137"},{"issue":"12","key":"S0219622021500449BIB010","doi-asserted-by":"crossref","first-page":"9227","DOI":"10.1007\/s00500-019-04449-7","volume":"24","author":"Li X.","year":"2020","journal-title":"Soft Computing"},{"key":"S0219622021500449BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0219622012500095"},{"issue":"4","key":"S0219622021500449BIB012","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1080\/01605682.2019.1705193","volume":"72","author":"Wang H.","year":"2020","journal-title":"Journal of the Operational Research Society"},{"key":"S0219622021500449BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109599"},{"volume-title":"The UCR time series classification archive","year":"2015","author":"Chen Y.","key":"S0219622021500449BIB015"},{"key":"S0219622021500449BIB016","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00293"},{"key":"S0219622021500449BIB017","first-page":"727","volume-title":"ICML 2000: Proc. 7th Int. 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