Giovanni Rossi
University of Bologna, Italy
Title: Objective function-based clustering via near-Boolean optimization
Biography
Biography: Giovanni Rossi
Abstract
Objective function-based clustering is here looked as a maximum-weight set partitioning combinatorial optimization problem, with the instance given by a pseudo-Boolean (set) function assigning real-valued cluster scores (or costs, in case of minimization) to data subsets, while on every partition of data the global objective function takes the value given by the sum over clusters (or blocks) of their individual score. The instance may thus maximally consist of 2n reals, where n is the number of data, although in most cases the scores of singletons and pairs also fully determine the scores of larger clusters, in which the pseudo- Boolean function is quadratic. This work proposes to quantify the cluster score of fuzzy data subsets by means of the polynomial MLE (multi-linear extension) of pseudo-Boolean functions, thereby translating the original discrete optimization problem into a continuous framework. After analyzing in these terms, the modularity maximization problem, two further examples of quadratic cluster score functions for graph clustering are proposed, while also analyzing greedy (local and global) search strategies.