A new research paper explores the relationship between K-Means clustering and normalized radial basis function (RBF) assignments, proposing that K-Means can be viewed as the zero-temperature limit of these assignments. The study details how relaxing K-Means assignments with a Shannon entropy penalty leads to normalized Gaussian RBF responsibilities and a reduced objective function that converges to the K-Means distortion. The paper also demonstrates that alternating minimization acts as a preconditioned gradient method on this objective, with its hard limit being Lloyd's algorithm, and introduces Entmax-1.5 as a method to recover hard assignments and Lloyd's update under specific conditions. AI
IMPACT This research provides a theoretical link between a fundamental clustering algorithm and differentiable learning methods, potentially enabling new approaches in unsupervised learning and representation learning.
RANK_REASON The cluster contains a single academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=1.0]
- arXiv
- entmax
- Felipe De Jesus Arredondo
- k-means clustering
- Lloyd's algorithm
- Normalized RBF Assignments
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