Developments on Solutions of the Normalized-Cut-Clustering Problem Without Eigenvectors

Normalized-cut clustering (NCC) is a benchmark graph-based approach for unsupervised data analysis. Since its traditional formulation is a quadratic form subject to orthogonality conditions, it is often solved within an eigenvector-based framework. Nonetheless, in some cases the calculation of eigenvectors is prohibitive or unfeasible due to the involved computational cost – for instance, when dealing with high dimensional data. In this work, we present an overview of recent developments on approaches to solve the NCC problem with no requiring the calculation of eigenvectors. Particularly, heuristic-search and quadratic-formulation-based approaches are studied. Such approaches are elegantly deduced and explained, as well as simple ways to implement them are provided.