Branch-and-Bound for Model Selection and Its Computational Complexity

Branch-and-bound methods are used in various data analysis problems, such as clustering, seriation and feature selection. Classical approaches of branch-and-bound based clustering search through combinations of various partitioning possibilities to optimize a clustering cost. However, these approaches are not practically useful for clustering of image data where the size of data is large. Additionally, the number of clusters is unknown in most of the image data analysis problems. By taking advantage of the spatial coherency of clusters, we formulate an innovative branch-and-bound approach, which solves clustering problem as a model-selection problem. In this generalized approach, cluster parameter candidates are first generated by spatially coherent sampling. A branch-and-bound search is carried out through the candidates to select an optimal subset. This paper formulates this approach and investigates its average computational complexity. Improved clustering quality and robustness to outliers compared to conventional iterative approach are demonstrated with experiments.