Influence Function and Robust Variant of Kernel Canonical Correlation Analysis.

Area of Science:

• Machine Learning
• Statistical Learning Theory
• Data Science

Background:

• Unsupervised kernel methods often use kernel covariance operators (kernel CO) or kernel cross-covariance operators (kernel CCO).
• These methods are vulnerable to data contamination, even with bounded positive definite kernels.
• Robust statistical methods for unsupervised kernel learning are scarce.

Purpose of the Study:

• To develop robust kernel covariance and cross-covariance operators.
• To derive the influence function (IF) for robust kernel CCO and standard kernel CCA.
• To introduce a robust kernel CCA method less sensitive to noise.

Main Methods:

• Proposed robust kernel CO and robust kernel CCO using a generalized loss function.
• Derived the influence function (IF) for robust kernel CCO and standard kernel CCA.
• Developed a robust kernel CCA method based on the proposed operators.

Main Results:

• The derived IF for standard kernel CCA effectively identifies influential outliers in data.
• The proposed robust kernel CCA demonstrates reduced sensitivity to noise compared to standard kernel CCA.
• Experiments on synthetic and real-world imaging genetics data validate the robustness and performance.

Conclusions:

• The novel robust kernel operators and robust kernel CCA offer improved statistical unsupervised learning.
• The derived influence function is valuable for outlier detection in kernel CCA.
• The principles can be extended to other kernel-based methods sensitive to kernel CO or CCO.