Optimized Mahalanobis-Taguchi System for High-Dimensional Small Sample Data Classification.

Area of Science:

• Multivariate statistical analysis
• Machine learning
• Data mining

Background:

• The Mahalanobis-Taguchi system (MTS) is effective for large or unbalanced datasets but struggles with high-dimensional, small-sample data.
• Challenges include covariance matrix instability and unreliable feature selection in high-dimensional, small-sample scenarios.

Purpose of the Study:

• To optimize the Mahalanobis-Taguchi system (MTS) for improved classification of high-dimensional, small-sample data.
• Address the instability issues in covariance matrix inversion and feature selection within MTS.

Main Methods:

• Developed a modified Mahalanobis distance (RS-MD) using regularization and smoothing to mitigate covariance matrix instability.
• Introduced a two-stage feature selection method combining the minimum redundancy-maximum relevance (mRMR) algorithm with signal-to-noise ratio (SNR) and orthogonal tables.

Main Results:

• The regularization and smoothing-based Mahalanobis distance (RS-MD) demonstrated increased robustness compared to traditional methods.
• The two-stage feature selection significantly enhanced the effectiveness of variable selection in MTS.
• Validated on five UCI datasets, showing improved performance.

Conclusions:

• The optimized MTS provides a robust and effective solution for classifying high-dimensional, small-sample data.
• Outperformed classical MTS and other machine learning algorithms in email classification tasks (Spambase dataset).
• Highlights the potential of integrating regularization, smoothing, and advanced feature selection techniques into MTS.