Minimum regularized covariance determinant and principal component analysis-based method for the identification of...

Area of Science:

• Statistics
• Data Mining
• Machine Learning

Background:

• High Leverage Points (HLPs) identification is crucial in statistical analysis.
• Existing Robust Mahalanobis Distance (RMD) methods, like RMD-MRCD, struggle with high-dimensional data.
• Increased independent variables (p) degrade RMD-MRCD performance.

Purpose of the Study:

• Propose a novel method, RMD-MRCD-PCA, for identifying HLPs in high-dimensional sparse data.
• Address the performance limitations of RMD-MRCD as dimensionality increases.
• Enhance the robustness and applicability of HLP identification techniques.

Main Methods:

• Developed RMD-MRCD-PCA by integrating Principal Component Analysis (PCA) into the Minimum Regularized Covariance Determinant (MRCD) algorithm.
• The PCA component shrinks the covariance matrix, ensuring invertibility for RMD computation.
• Utilized simulation studies and two real datasets for comparative analysis.

Main Results:

• RMD-MRCD-PCA demonstrates comparable performance to RMD-MRCD for p ≈ 200.
• RMD-MRCD performance degrades significantly for p > 200, especially at p = 700.
• Robust PCA (ROBPCA) shows ineffectiveness with less than 20% contamination due to swamping issues.

Conclusions:

• RMD-MRCD-PCA offers a robust solution for HLP identification in high-dimensional datasets.
• The proposed method overcomes the limitations of traditional RMD-MRCD as dimensionality grows.
• RMD-MRCD-PCA provides a more reliable alternative to ROBPCA in certain contamination scenarios.