Convex Clustering and Lyapunov Functional Minimization in High Dimensional Optimization

The piecewise constant Mumford-Shah model is used to investigate a multi-class segmentation issue inside a graph framework; this topic is pertinent to an adjacent area of study. We provide an effective strategy based on the MBO approach for the graph form of the Mumford-Shah model. In theoretical study, it is shown that when algorithm complexity increases, a Lyapunov functional decreases. Also, for big datasets, we estimate the eigenvectors of the graph Laplacian efficiently using a limited subset of the weight matrix using the Nyström extension technique, which helps to lower the computational cost. Finally, we apply the suggested method to the issue of chemical plume identification in hyper spectral video data. We presented graph-based clustering methods that drastically cut down on processing time for massive datasets. A straightforward and very parallelizable approach to multiway graph partitioning, our incremental reseeding clustering technique, is presented in the final chapter. We demonstrate via experiments that our method achieves top-notch results for cluster purity on common benchmark datasets. The method is also orders of magnitude faster than competing approaches.