Modal clustering of matrix-variate data

Area of Science:

• Statistics
• Data Mining
• Machine Learning

Background:

• Modal clustering links data groups to density modes.
• Matrix-valued data is increasingly common in various scientific fields.
• Existing methods struggle with the complexity of matrix-variate data.

Purpose of the Study:

• To generalize modal clustering to the matrix-variate setting.
• To develop nonparametric estimators for matrix-variate distributions.
• To propose a robust mode-finding procedure for high-dimensional data.

Main Methods:

• Utilized kernel methods for nonparametric estimation of matrix-variate distributions.
• Developed a generalized mean-shift procedure for mode identification.
• Implemented locally adaptive solutions to address high dimensionality.

Main Results:

• Introduced novel nonparametric estimators for matrix-variate distributions.
• Demonstrated the asymptotic properties of the proposed estimators.
• Showcased the effectiveness of the generalized mean-shift procedure through simulations and real-world applications.

Conclusions:

• The proposed method provides a powerful tool for density-based clustering of matrix-variate data.
• The approach handles high-dimensional data effectively, outperforming competitors in simulations.
• Successful application to real-world datasets highlights its practical utility.