Two-Way Regularized Fuzzy Clustering of Multiple Correspondence Analysis

Area of Science:

• Multivariate Statistics
• Data Mining
• Machine Learning

Background:

• Multiple Correspondence Analysis (MCA) is effective for analyzing relationships among categorical variables.
• Existing MCA clustering methods often use hard classification, limiting interpretation by assigning observations/categories to single clusters.
• Two-way MCA clustering offers better interpretability by linking observation subgroups with variable category subsets.

Purpose of the Study:

• To propose a novel two-way fuzzy clustering approach for Multiple Correspondence Analysis (MCA).
• To relax the hard classification constraint in existing two-way MCA clustering methods.
• To enable partial cluster memberships for both observations and variable categories.

Main Methods:

• Integration of Multiple Correspondence Analysis (MCA) with fuzzy k-means clustering.
• Simultaneous classification of observation subgroups and variable category subsets into common clusters.
• Utilization of regularized fuzzy k-means for automatic determination of cluster fuzziness.

Main Results:

• The proposed two-way fuzzy clustering of MCA effectively handles partial memberships, offering a more nuanced analysis.
• Performance evaluation using simulated and real data demonstrates the approach's viability compared to existing methods.
• The method provides enhanced interpretability by allowing observations and variable categories to belong to multiple clusters.

Conclusions:

• Two-way fuzzy clustering of MCA offers a flexible and interpretable alternative to hard classification methods.
• This approach advances the analysis of heterogeneous subclusters within populations based on categorical data.
• The method holds potential for improved classification and understanding of complex data structures.