An Approach to Canonical Correlation Analysis Based on Rényi's Pseudodistances

Area of Science:

• Multivariate statistics
• Data analysis
• Machine learning

Background:

• Canonical Correlation Analysis (CCA) identifies linear relationships between two variable sets.
• Existing methods like Information Canonical Correlation Analysis (ICCA) have limitations regarding outlier sensitivity.

Purpose of the Study:

• To introduce a novel method, RP canonical analysis (RPCCA), for detecting linear and non-linear relationships.
• To develop a robust alternative to ICCA that is less affected by outliers and data contamination.

Main Methods:

• Developed RPCCA by maximizing a measure based on Rényi's pseudodistances (RP).
• Provided estimation techniques for RPCCA and proved the consistency of estimated canonical vectors.
• Described a permutation test for identifying significant canonical variable pairs.

Main Results:

• RPCCA successfully detects both linear and non-linear relationships.
• The method demonstrates inherent robustness against outliers and data contamination.
• Empirical and theoretical analyses confirm the robustness properties of RPCCA.

Conclusions:

• RPCCA is a competitive and robust alternative to ICCA.
• The enhanced robustness makes RPCCA suitable for datasets with potential outliers.