Likelihood-ratio-based verification in high-dimensional spaces.

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• High-dimensional data presents challenges in statistical estimation, known as the curse of dimensionality.
• A key issue is the singularity problem: covariance matrices become non-full rank, hindering inversion for likelihood ratio-based verification systems.

Purpose of the Study:

• To evaluate the effectiveness of Principle Component Analysis (PCA) in mitigating high-dimensionality issues for second-order statistics (SOS) estimation.
• To propose and validate a novel method, fixed-point eigenwise correction, as a superior alternative to PCA for high-dimensional data analysis.

Main Methods:

• Theoretical analysis of second-order statistics (SOS) estimation in high-dimensional spaces.
• Comparative performance evaluation of PCA, Euclidean distance-based methods, and the proposed fixed-point eigenwise correction.

Main Results:

• Principle Component Analysis (PCA) is shown to be suboptimal for verification systems when high dimensionality is the primary error source.
• PCA is outperformed by Euclidean distance methods in moderate dimensions and fails in very high dimensions.
• The proposed fixed-point eigenwise correction method demonstrates near-optimal performance across dimensions.

Conclusions:

• Traditional PCA-based dimensionality reduction is inadequate for SOS estimation in high-dimensional verification systems.
• The fixed-point eigenwise correction offers a robust and near-optimal solution for handling the curse of dimensionality in these applications.