This project explores several MCMC sampling procedures and applies them to (1) the image denoising problem by assuming an underlying Ising model, and (2) to a combinatorial optimization problem, namely TSP.
Implementation of the DA algorithm according to Deterministic annealing for clustering, compression, classification, regression, and related optimization problems and empirical analysis of its phase transition behaviour.
This project explores a tecnhique called Constant Shift Embedding which embeds pairwise clustering problems in vector spaces while preserving the cluster structure, as explained in Optimal cluster preserving embedding of nonmetric proximity data.
This code applies MFA, as introduced in An Introduction to Variational Methods for Graphical Models, to two problem settings: (1) the 2D Ising model for image denoising, and (2) to solve Smooth-K-means, a slighly different version of K-means, in which smoothness constraints on the solution space make the problem combinatorially harder.