K-Means as a Radial Basis function Network: a Variational and Gradient-based Equivalence [R]

K Means is basically an RBF network I have been working on a formulation of K Means as a continuous optimization problem instead of a discrete algorithm. The idea is to replace hard assignments with soft responsibilities and define a smooth objective that preserves the clustering structure while making the system fully differentiable and trainable end to end. The main result is a Gamma convergence analysis showing that this objective recovers standard K Means in the zero temperature limit.