Legendre polynomial transformation and energy-weighted random forests for sequential data classification.

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.