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[2602.20857] Functional Continuous Decomposition
Summary
The paper introduces Functional Continuous Decomposition (FCD), a novel framework for analyzing non-stationary time-series data using parametric optimization, enhancing accuracy and speed in various applications.
Why It Matters
FCD addresses limitations in traditional smoothing algorithms by providing a continuous optimization approach that improves the analysis of time-series data across multiple fields, including physics and machine learning. Its ability to enhance CNN performance underscores its potential impact on data-driven applications.
Key Takeaways
- FCD offers a JAX-accelerated framework for continuous optimization of time-series data.
- It achieves up to $C^1$ continuous fitting, improving interpretability of data patterns.
- FCD can significantly enhance CNN performance, leading to faster convergence and higher accuracy.
- The framework is applicable in diverse fields such as finance, medicine, and physics.
- FCD demonstrates an average SRMSE of 0.735 and processes 1,000 data points in 0.47 seconds.
Electrical Engineering and Systems Science > Signal Processing arXiv:2602.20857 (eess) [Submitted on 24 Feb 2026] Title:Functional Continuous Decomposition Authors:Teymur Aghayev View a PDF of the paper titled Functional Continuous Decomposition, by Teymur Aghayev View PDF HTML (experimental) Abstract:The analysis of non-stationary time-series data requires insight into its local and global patterns with physical interpretability. However, traditional smoothing algorithms, such as B-splines, Savitzky-Golay filtering, and Empirical Mode Decomposition (EMD), lack the ability to perform parametric optimization with guaranteed continuity. In this paper, we propose Functional Continuous Decomposition (FCD), a JAX-accelerated framework that performs parametric, continuous optimization on a wide range of mathematical functions. By using Levenberg-Marquardt optimization to achieve up to $C^1$ continuous fitting, FCD transforms raw time-series data into $M$ modes that capture different temporal patterns from short-term to long-term trends. Applications of FCD include physics, medicine, financial analysis, and machine learning, where it is commonly used for the analysis of signal temporal patterns, optimized parameters, derivatives, and integrals of decomposition. Furthermore, FCD can be applied for physical analysis and feature extraction with an average SRMSE of 0.735 per segment and a speed of 0.47s on full decomposition of 1,000 points. Finally, we demonstrate that a Convolution...
