[Paper Review] Geographically Weighted Canonical Correlation Analysis: Local Spatial Associations Between Two Sets of Variables

Zhenzhi Jiao, Angela Yao+2 more|arXiv (Cornell University)|Feb 10, 2026

Spatial and Panel Data Analysis0 citations

TL;DR

The paper proposes Geographically Weighted Canonical Correlation Analysis (GWCCA) to localize Canonical Correlation Analysis by weighting observations by spatial distance, enabling location-specific multivariate spatial associations between two variable sets. It demonstrates GWCCA with synthetic data and a US county-level health case study.

ABSTRACT

This article critically assesses the utility of the classical statistical technique of Canonical Correlation Analysis (CCA) for studying spatial associations and proposes a new approach to enhance it. Unlike bivariate correlation analysis, which focuses on the relationship between two individual variables, CCA investigates associations between two sets of variables by identifying pairs of linear combinations that are maximally correlated. CCA has strong potential for uncovering complex multivariate relationships that vary across geographic space. We propose Geographically Weighted Canonical Correlation Analysis (GWCCA) as a new technique for exploring local spatial associations between two sets of variables. GWCCA localizes standard CCA by weighting each observation according to its spatial distance from a target location, thereby estimating location-specific canonical correlations. The effectiveness of GWCCA in recovering spatial structure and capturing spatial effects is evaluated using synthetic data. A case study of US county-level health outcomes and social determinants of health further demonstrates the empirical capabilities of the proposed method. The results indicate that GWCCA has broad potential applications in spatial data-intensive fields such as urban planning, environmental science, public health, and transportation, where understanding local multivariate spatial associations is critical.

Motivation & Objective

• Motivate the need to study spatially varying multivariate associations beyond standard CCA.
• Propose GWCCA to localize CCA via spatial distance-based weighting.
• Evaluate GWCCA's ability to recover spatial structure using simulations and a health-related case study.

Proposed method

• Wrap CCA in a geographically weighted framework by weighting each observation by its distance to a target location.
• Estimate location-specific canonical correlations at each location.
• Assess performance with synthetic data to recover spatial structure.
• Demonstrate empirical capabilities via a US county-level health outcomes and social determinants case study.

Experimental results

Research questions

• RQ1 Can CCA be localized to capture spatially varying associations between two variable sets?
• RQ2 Do spatial weights enable GWCCA to recover underlying local multivariate spatial structure?
• RQ3 Is GWCCA effective in real-world spatial health data contexts such as county-level outcomes and determinants?

Key findings

• GWCCA localizes standard CCA to estimate location-specific canonical correlations.
• Synthetic-data experiments show GWCCA can recover spatial structure and capture spatial effects.
• A US county-level health outcomes and social determinants case study demonstrates GWCCA's empirical applicability.
• GWCCA has broad potential in spatial data-intensive fields like urban planning, environment, public health, and transportation.