https://doi.org/10.1140/epjs/s11734-025-01580-5
Regular Article
Time-series prediction with optimized non-affine fractal interpolations using neural network
VIT-AP University, 522 237, Amaravati, Andhra Pradesh, India
Received:
9
October
2024
Accepted:
14
March
2025
Published online:
15
April
2025
This paper implements modified optimization algorithms to fine-tune Iterated Function System (IFS) parameters, particularly focusing on the vertical scaling factor in Non-Affine Fractal Interpolation (NAFI) to enhance prediction accuracy. A modified numerical optimization algorithm, the Fractal Nelder–Mead Algorithm, is employed where the input vector is the vertical scaling factor. Similarly, modified stochastic algorithms, such as Fractal Particle Swarm Optimization Algorithm (FPSOA) and Fractal Differential Evolution Algorithm (FDEA), are applied with a specific implementation of the fitness function, which minimizes the Euclidean distance between a target fractal curve and the approximated fractal curves. A case study is carried out to quote the best forecasting method for NAFI. Three forecasting methodologies are examined: time-series forecasting using Autoregressive Integrated Moving Average Model (ARIMA), machine learning forecasting with Nu-Support Vector Regression (Nu-SVR), and feed-forward neural networks. While ARIMA and Nu-SVR encounter certain limitations, the neural network demonstrates superior performance. The effectiveness of these forecasting methods, when combined with fractal-based optimization techniques, is evaluated using statistical metrics such as root-mean-squared error (RMSE). This research provides novel insights into the integration of optimization techniques with predictive modeling, advancing both the theoretical landscape and practical applications of non-affine fractal interpolation and time-series forecasting.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
