Hyperparameter-Free Localized Simple Multiple Kernel K-means With Global Optimum.

Area of Science:

• Machine Learning
• Data Mining
• Clustering Algorithms

Background:

• Localized Simple Multiple Kernel k-means (SimpleMKKM) offers superior clustering but requires manual hyperparameter tuning for localization size.
• This hyperparameter dependency limits its practical use in diverse clustering tasks.
• Lack of clear guidelines for setting localization hyperparameters hinders SimpleMKKM adoption.

Purpose of the Study:

• To develop a hyperparameter-free version of localized SimpleMKKM.
• To enable automatic learning of optimal neighborhood parameters within the clustering framework.
• To enhance the practical applicability and robustness of localized kernel k-means clustering.

Main Methods:

• Parameterized neighborhood mask matrices as a quadratic combination of base matrices.
• Jointly learned neighborhood mask coefficients with clustering objectives.
• Formulated the optimization as minimizing an optimal value function and developed a gradient-based solver.
• Proved the differentiability and global optimality of the proposed solution.

Main Results:

• Introduced a novel hyperparameter-free localized SimpleMKKM algorithm.
• Demonstrated effectiveness through comprehensive experiments on benchmark datasets.
• Achieved competitive or superior performance compared to state-of-the-art clustering methods.
• Provided source code for reproducibility and further research.

Conclusions:

• The proposed hyperparameter-free localized SimpleMKKM effectively addresses the limitations of its predecessor.
• The method offers a more practical and robust clustering solution by eliminating manual hyperparameter tuning.
• The theoretical guarantees and experimental validation support its efficacy in various data clustering applications.