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We, instead, investigate adding such regularizations to the original cost function. We first consider the case where the regularization term is the sum of the squared size of the clusters, and then generalize it to adaptive regularization of the pairwise similarities. This leads to shifting (adaptively) the pairwise similarities which might make some of them negative. We then study the connection of this method to <jats:italic>Correlation Clustering<\/jats:italic> and then propose an efficient <jats:italic>local search<\/jats:italic> optimization algorithm with fast theoretical convergence rate to solve the new clustering problem. In the following, we investigate the shift of pairwise similarities on some common clustering methods, and finally, we demonstrate the superior performance of the method by extensive experiments on different datasets.<\/jats:p>","DOI":"10.1007\/s10994-022-06189-6","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T17:04:45Z","timestamp":1655917485000},"page":"2025-2051","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Shift of pairwise similarities for data clustering"],"prefix":"10.1007","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2912-7422","authenticated-orcid":false,"given":"Morteza","family":"Haghir Chehreghani","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"6189_CR1","doi-asserted-by":"crossref","unstructured":"Bailey, K. (1994). Numerical taxonomy and cluster analysis. 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No conflict of interest occurs.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This research is mainly focused on conceptual and methodological developments in unsupervised learning and clustering. Clustering is usually used for data management and exploratory data analytics. Thus, this contribution provides methods to further understand, explore and explain the data and obtain deeper insights. Such possibilities can be used for example to understand gender-specific features, data irregularities, private and sensitive information and explainability aspects. On the other hand, the use of clustering for data management and summarization provides a systematic way to compress the data to yield more efficient data precessing in terms of energy and memory usage. This, itself, can be helpful for better environmental conditions. These properties are critical when dealing with large amount of data, in particular for environment friendly solutions. Finally, we would like to emphasize that in this work the experimental studies use the datasets which do not contain any private and sensitive information.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"Not Applicable. There is no human study in this research.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not Applicable. No human study is performed in this research. There is no sensitive information.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The code will be available through the author\u2019s home page and will be maintained there with a reference to this publication.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}