{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T03:00:10Z","timestamp":1774839610995,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T00:00:00Z","timestamp":1689724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2022YFF0801200"],"award-info":[{"award-number":["2022YFF0801200"]}]},{"name":"National Key Research and Development Program of China","award":["2022YFF0801203"],"award-info":[{"award-number":["2022YFF0801203"]}]},{"name":"National Key Research and Development Program of China","award":["41972306"],"award-info":[{"award-number":["41972306"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFF0801200"],"award-info":[{"award-number":["2022YFF0801200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022YFF0801203"],"award-info":[{"award-number":["2022YFF0801203"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41972306"],"award-info":[{"award-number":["41972306"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Time series data typically exhibit high dimensionality and complexity, necessitating the use of specific approximation methods to perform computations on the data. The currently employed compression methods suffer from varying degrees of feature loss, leading to potential distortions in similarity measurement results. Considering the aforementioned challenges and concerns, this paper proposes a double mean representation method, SAX-DM (Symbolic Aggregate Approximation Based on Double Mean Representation), for time series data, along with a similarity measurement approach based on SAX-DM. Addressing the trade-off between compression ratio and accuracy in the improved SAX representation, SAX-DM utilizes the segment mean and the segment trend distance to represent corresponding segments of time series data. This method reduces the dimensionality of the original sequences while preserving the original features and trend information of the time series data, resulting in a unified representation of time series segments. Experimental results demonstrate that, under the same compression ratio, SAX-DM combined with its similarity measurement method achieves higher expression accuracy, balanced compression rate, and accuracy, compared to SAX-TD and SAX-BD, in over 80% of the UCR Time Series dataset. This approach improves the efficiency and precision of similarity calculation.<\/jats:p>","DOI":"10.3390\/a16070347","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T21:21:46Z","timestamp":1689801706000},"page":"347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Similarity Measurement and Classification of Temporal Data Based on Double Mean Representation"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6280-8791","authenticated-orcid":false,"given":"Zhenwen","family":"He","sequence":"first","affiliation":[{"name":"School of Computer Science, China University of Geosciences (Wuhan), 388 Lumo Road, Wuhan 430074, China"}]},{"given":"Chi","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Geosciences (Wuhan), 388 Lumo Road, Wuhan 430074, China"}]},{"given":"Yunhui","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Computer Science, China University of Geosciences (Wuhan), 388 Lumo Road, Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"ref_1","first-page":"44","article-title":"Overview of similarity measurement and indexing methods for geoscience time series Big data","volume":"39","author":"He","year":"2020","journal-title":"Bull. Geol. Sci. Technol."},{"key":"ref_2","unstructured":"Agrawal, R., Faloutsos, C., and Swami, A. (1993, January 13\u201315). Efficient similarity search in sequence databases. Proceedings of the Foundations of Data Organization and Algorithms: 4th International Conference, FODO\u201993, Chicago, IL, USA."},{"key":"ref_3","unstructured":"Chan, K.P., and Fu AW, C. (1999, January 23\u201326). Efficient time series matching by wavelets. Proceedings of the 15th International Conference on Data Engineering (Cat. No. 99CB36337), Sydney, Australia."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1145\/253262.253332","article-title":"Efficiently supporting ad hoc queries in large datasets of time sequences","volume":"26","author":"Korn","year":"1997","journal-title":"SIGMOD Rec."},{"key":"ref_5","unstructured":"Yi, B.K., and Faloutsost, C. (2023, February 10). Fast Time Sequence Indexing for Arbitrary Lp Norms. Available online: https:\/\/www.vldb.org\/conf\/2000\/P385.pdf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.engappai.2007.04.009","article-title":"Representing financial time series based on data point importance","volume":"21","author":"Fu","year":"2008","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cai, Y., and Ng, R.T. (2004, January 13\u201318). Indexing Spatio-Temporal Trajectories with Chebyshev Polynomials. Proceedings of the 2004 ACM SIGMOD International Conference on Management of Data, Paris, France.","DOI":"10.1145\/1007568.1007636"},{"key":"ref_8","unstructured":"Chen, Q., Chen, L., Lian, X., Liu, Y., and Yu, X. (2007, January 23\u201327). Indexable PLA for Efficient Similarity Search. Proceedings of the 33rd International Conference on Very Large Data Bases, Vienna, Austria."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TKDE.2012.88","article-title":"The Move-Split-Merge Metric for Time Series","volume":"25","author":"Stefan","year":"2013","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.ins.2015.04.007","article-title":"Dynamic time warping under pointwise shape context","volume":"315","author":"Zhang","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_11","first-page":"239","article-title":"An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback","volume":"98","author":"Keogh","year":"1998","journal-title":"InKdd"},{"key":"ref_12","unstructured":"Keogh, E.J. (2023, February 16). A Simple Dimensionality Reduction Technique for Fast Similarity Search in Large Time Series Databases. Available online: http:\/\/www.cs.ucr.edu\/~eamonn\/pakdd200_keogh.pdf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1145\/568518.568520","article-title":"Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases","volume":"27","author":"Chakrabarti","year":"2002","journal-title":"ACM Trans. Database Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lin, J., Keogh, E.J., Lonardi, S., and Chiu, B. (2003, January 13). A symbolic representation of time series, with implications for streaming algorithms. Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery, San Diego, CA, USA.","DOI":"10.1145\/882082.882086"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10618-007-0064-z","article-title":"Experiencing SAX: A novel symbolic representation of time series","volume":"15","author":"Lin","year":"2007","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.neucom.2014.01.045","article-title":"An improvement of symbolic aggregate approximation distance measure for time series","volume":"138","author":"Sun","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"He, Z., Long, S., Ma, X., and Zhao, H. (2020). A Boundary Distance-Based Symbolic Aggregate Approximation Method for Time Series Data. Algorithms, 13.","DOI":"10.3390\/a13110284"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"He, Z., Zhang, C., Ma, X., and Liu, G. (2021). Hexadecimal Aggregate Approximation Representation and Classification of Time Series Data. Algorithms, 14.","DOI":"10.3390\/a14120353"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yang, D., and Kang, Y. (2022). Distance- and Momentum-Based Symbolic Aggregate Approximation for Highly Imbalanced Classification. Sensors, 22.","DOI":"10.3390\/s22145095"},{"key":"ref_20","first-page":"86","article-title":"Time series data symbol aggregation approximation method for fusing trend information","volume":"40","author":"Huang","year":"2023","journal-title":"Appl. Res. Comput."},{"key":"ref_21","unstructured":"Ratanamahatana, C., Keogh, E., Bagnall, A.J., and Lonardi, S. (2005). Advances in Knowledge Discovery and Data Mining, Proceedings of the 9th Pacific-Asia Conference, PAKDD 2005, Hanoi, Vietnam, 18\u201320 May 2005, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1007\/s10618-014-0349-y","article-title":"Learning a symbolic representation for multivariate time series classification","volume":"29","author":"Baydogan","year":"2015","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_23","unstructured":"Azzouzi, M., and Nabney, I.T. (1998). Neural Networks for Signal Processing VIII, Proceedings of the 1998 IEEE Signal Processing Society Workshop (Cat. No. 98TH8378), Cambridge, UK, 31 August\u20133 September 1998, IEEE."},{"key":"ref_24","first-page":"514","article-title":"Predictability of Music Descriptor Time Series and its Application to Cover Song Detection","volume":"20","author":"Serra","year":"2012","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1007\/s10618-015-0425-y","article-title":"Time series representation and similarity based on local autopatterns","volume":"30","author":"Baydogan","year":"2016","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1007\/s10115-018-1264-0","article-title":"Similarity measures for time series data classification using grid representation and matrix distance","volume":"60","author":"Ye","year":"2019","journal-title":"Knowl. Inf. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Su, Z., Liu, Q., Zhao, C., and Sun, F. (2022). A Traffic Event Detection Method Based on Random Forest and Permutation Importance. Mathematics, 10.","DOI":"10.3390\/math10060873"},{"key":"ref_28","first-page":"6","article-title":"The UCR Time Series Archive","volume":"6","author":"Dau","year":"2019","journal-title":"IEEE\/CAA J. Autom. Sin."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/7\/347\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:14:45Z","timestamp":1760127285000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/7\/347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,19]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["a16070347"],"URL":"https:\/\/doi.org\/10.3390\/a16070347","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,19]]}}}