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Related Experiment Video

Updated: Jan 14, 2026

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model
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Legendre polynomial transformation and energy-weighted random forests for sequential data classification.

Oyebayo Ridwan Olaniran1,2, Fatimah M Alghamdi3, Nada MohammedSaeed Alharbi4

  • 1Department of Statistics, Faculty of Physical Sciences, University of Ilorin, PMB 1515, Ilorin, Kwara State, Nigeria.

Scientific Reports
|October 22, 2025
PubMed
Summary

The Legendre Energy-Weighted Random Forest (LEW-RF) accurately classifies sequential data, offering improved accuracy and speed over traditional methods. This novel approach enhances temporal trend analysis for diverse applications.

Keywords:
Legendre Energy-Weighted Random Forest (LEW-RF)Legendre polynomialsLegendre transformationsRandom Forest (RF)Sequential data classificationTemporal dependencies

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Area of Science:

  • Machine Learning
  • Data Science
  • Signal Processing

Background:

  • Accurate classification of sequential data (time series, sensor streams) is vital for environmental monitoring and industrial fault detection.
  • Traditional methods struggle with temporal dependencies and noise; deep learning faces computational and interpretability challenges.
  • Existing approaches often fail to capture complex temporal patterns effectively.

Purpose of the Study:

  • Introduce the Legendre Energy-Weighted Random Forest (LEW-RF), a novel framework for sequential data classification.
  • Address limitations of traditional and deep learning methods in handling temporal dependencies, noise, and interpretability.
  • Enhance the accuracy and efficiency of sequential data analysis.

Main Methods:

  • Integrate Legendre polynomial transformations with Random Forest (RF) for feature extraction.
  • Utilize low-degree Legendre coefficients to capture discriminative temporal trends (e.g., drifts, anomalies).
  • Employ feature-wise energies to guide RF splits, enhancing robustness to noise and irregular sampling.

Main Results:

  • LEW-RF achieved 81.2% accuracy and 86.4% AUC on synthetic data, outperforming conventional RF by 5.3% and running 126x faster than BiLSTM.
  • On an eight-hour ozone dataset, LEW-RF reached 97.0% accuracy, 99.6% recall, and 99.8% AUC.
  • LEW-RF demonstrated superior performance over conventional RF (1.4% accuracy gain) and was 228x faster than BiLSTM on the ozone dataset.
  • Identified critical temporal sensors (T13-T15) crucial for photochemical pollution events, aligning with atmospheric science principles.

Conclusions:

  • LEW-RF offers a robust and efficient solution for sequential data classification, outperforming existing methods.
  • The Legendre energy feature is theoretically linked to class separability, providing noise robustness.
  • LEW-RF enhances interpretability in sequential data analysis, with practical applications in environmental monitoring.