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Classical and fast parameters tuning in nearest neighbors with stop condition

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Abstract

In this paper, we study the convergence of the algorithms employed by Classical Parameters Tuning in Nearest Neighbors (CPTO-WNN) and Fast Parameters Tuning in Nearest Neighbors (FPTO-WNN). CPTO-WNN and FPTO-WNN are two methodologies that perform the selection of weighted nearest neighbors parameters in time series setting. To do so, each methodology employs an algorithm named WNNoptimization. The WNNoptimization algorithm employs a method inspired by time series cross validation to pick automatically the weighted nearest neighbors parameters. Practically, it computes the global accuracy measure over the test sets, for different values of weighted nearest neighbors parameters and returns the ones for which the accuracy measure is minimal. Compared to CPTO-WNN, FPTO-WNN presents the advantage of reducing time complexity. However, when we are faced with many iterations, both methods raise concerns about computational time. One solution is to introduce a stop condition if the algorithms are convergent. Real data examples on retail and food services sales in the USA and milk production in the UK are analyzed to demonstrate the convergence of the algorithms. As a result, we propose a stop condition allowing the reduction of time complexity while maintaining a good precision. We compare the forecasting performance and time complexity of CPTO-WNN and FPTO-WNN after implementing the proposed stop condition. Experiments show that the introduction of the proposed stop condition provides good accuracy along with lower computational time.

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Data Availability

For our analysis, the Retail and Food Services Sales in the USA data that support the finding of this study are obtained from the United States Census Bureau Database, available at: https://www.census.gov/retail/index.html. Cow’s Milk Production in the UK are provided by Eurostat, which are available at: http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=apro_mk_colm &lang=en.

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Authors and Affiliations

  1. Mohammed V University in Rabat, Rabat, Morocco

    Samya Tajmouati

  2. Department of Mathematics, Faculty of Sciences, Ibn Tofail University, Kénitra, Morocco

    Bouazza El Wahbi

  3. Department of Economics and Management, Abdelmalek Essaâdi University, FSJES, Tétouan, Morocco

    Mohamed Dakkon

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  1. Samya Tajmouati
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  2. Bouazza El Wahbi
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  3. Mohamed Dakkon
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Contributions

ST developped CPTO-WNN and FPTO-WNN methodologies. ST, BEW, and MD noticed the convergence of these methodologies. ST proposed the stop condition allowing the reduction of time complexity without loss of precision. BEW and MD supervised the new methods as well as their application on real time series and approved them.

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Correspondence to Samya Tajmouati.

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Tajmouati, S., El Wahbi, B. & Dakkon, M. Classical and fast parameters tuning in nearest neighbors with stop condition. OPSEARCH 60, 1063–1081 (2023). https://doi.org/10.1007/s12597-023-00650-3

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