Cluster-Adaptive Feature Extraction and its Theoretical Foundation with Minkowski Weighted k-Means
arXiv:2603.25958v2 Announce Type: replace Abstract: The Minkowski weighted $k$-means ($mwk$-means) algorithm extends classical $k$-means by incorporating feature weights and a Minkowski distance. We first show that the $mwk$-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent $p$. This formulation reveals how $p$ controls the transition between selective and uniform use of features. Using this representation, we derive bounds for the objective function and characterise the structure of the feature weigh
This paper refines a theoretical foundation for advanced machine learning algorithms like k-means, which is crucial as AI systems become more complex and require greater interpretability and efficiency.
Improved theoretical understanding of clustering algorithms can lead to more robust, efficient, and interpretable AI models, impacting various downstream applications from scientific discovery to predictive analytics.
The explicit formulation of Minkowski weighted k-means objective as a power-mean aggregation offers a new lens for understanding and controlling feature selection in clustering, potentially enabling more adaptive model development.
- · AI/ML researchers
- · Data scientists
- · Industries relying on pattern recognition
- · Developers using less optimized traditional clustering methods
More efficient and accurate data clustering in advanced analytical systems.
Improved performance in areas like bioinformatics, fraud detection, and customer segmentation through better feature utilization.
Acceleration of research into self-supervised learning and adaptive AI, leading to more generalizable and autonomous AI agents.
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Read at arXiv cs.LG