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This paper presents a comparative analysis of two machine learning models, k-nearest neighbors (k-NN) regression and Decision Tree (DT), for scattered data interpolation and approximation. The models are evaluated based on coefficient of determination ( \(R^2\) ), root mean square error (RMSE), and maximum error. The computation and prediction times are also recorded. All results are obtained through MATLAB implementation. The findings demonstrate that DT consistently outperforms k-NN in terms of accuracy, achieving higher \(R^2\) values, lower RMSE, and reduced maximum error. The hierarchical structure of DT allows it to efficiently capture complex, non-linear relationships within the data, resulting in smoother and more accurate approximation surfaces. Additionally, DT shows better computational efficiency, with significantly faster prediction times compared to k-NN. While k-NN remains useful for highly dense and evenly distributed datasets, DT proves to be a more reliable choice for scattered data. Future work will involve evaluating a broader range of machine learning techniques, leveraging larger datasets, and exploring real-world applications. Furthermore, hyperparameter optimization, ensemble methods, and parallelization strategies will be investigated to further enhance the performance and scalability of DT for large-scale data approximation tasks.

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Scattered Data Interpolation and Approximation Using Machine Learning: k-NN and DT Approaches

  • 会议论文

  • 发表日期：

    2026年

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  • Owen Tamin,
  • Samsul Ariffin Abdul Karim,
  • Jumat Sulaiman,
  • Ervin Gubin Moung,
  • Faheem Khan,
  • Aslina Baharum,
  • Farkhana Binti Muchtar

摘要

This paper presents a comparative analysis of two machine learning models, k-nearest neighbors (k-NN) regression and Decision Tree (DT), for scattered data interpolation and approximation. The models are evaluated based on coefficient of determination ( \(R^2\) ), root mean square error (RMSE), and maximum error. The computation and prediction times are also recorded. All results are obtained through MATLAB implementation. The findings demonstrate that DT consistently outperforms k-NN in terms of accuracy, achieving higher \(R^2\) values, lower RMSE, and reduced maximum error. The hierarchical structure of DT allows it to efficiently capture complex, non-linear relationships within the data, resulting in smoother and more accurate approximation surfaces. Additionally, DT shows better computational efficiency, with significantly faster prediction times compared to k-NN. While k-NN remains useful for highly dense and evenly distributed datasets, DT proves to be a more reliable choice for scattered data. Future work will involve evaluating a broader range of machine learning techniques, leveraging larger datasets, and exploring real-world applications. Furthermore, hyperparameter optimization, ensemble methods, and parallelization strategies will be investigated to further enhance the performance and scalability of DT for large-scale data approximation tasks.