(Theoretical project) Learning Piecewise-Constant Functions to Classify and Cluster
Classification and clustering are some of the most important objectives in supervised and unsupervised learning, respectively. Interestingly, in both scenarios, the learning scheme eventually produces a piecewise-constant function. This remarkable property allows one to analyze them jointly. The goal of this project is to develop a variational framework to estimate piecewise-constant functions and to derive an efficient learning algorithm, built as a module. One can then also use this module in deep neural networks and compare the performance with classical setups for various applications of classification and clustering.