Variable Projection Support Vector Machines and Some Applications Using Adaptive Hermite Expansions.

Area of Science:

• Machine Learning
• Signal Processing
• Biomedical Engineering

Background:

• Classical Support Vector Machines (SVM) are powerful classification tools.
• Feature extraction often requires separate, complex processes.
• Real-time anomaly detection in sensor data presents significant challenges.

Purpose of the Study:

• To introduce a generalized SVM algorithm, the variable projection SVM (VP-SVM).
• To develop an integrated feature extraction and classification system.
• To evaluate VP-SVM for real-world anomaly detection tasks.

Main Methods:

• Developed the variable projection support vector machine (VP-SVM) algorithm.
• Utilized adaptive Hermite functions for orthogonal projections.
• Investigated nonlinear kernels and the primal optimization form.
• Implemented discrete orthogonal adaptive Hermite functions for computational efficiency.

Main Results:

• VP-SVM demonstrated effectiveness in anomaly detection for accelerometer and ECG data.
• Achieved results comparable to state-of-the-art methods.
• Validated real-time application feasibility through microcontroller implementation.
• Highlighted VP-SVM's lightweight architecture and interpretability.

Conclusions:

• VP-SVM offers a robust and efficient approach to classification and anomaly detection.
• The integration of feature extraction within the VP-SVM framework simplifies complex signal processing tasks.
• The method is suitable for real-time applications, particularly in sensor data analysis.