Recent Advances in Modularity Optimization and Their Application in Retailing

In this contribution we report on three recent advances in modularity optimization, namely:
1. The randomized greedy (RG) family of modularity optimization algorithms are state-of-the-art graph clustering algorithms which are near optimal, fast, and scalable.
2. The extension of the RG family to multi-level clustering.
3. A new entropy based cluster index which allows the detection of the proper clustering levels and of stable core clusters at each level.
Last, but not least, several marketing applications of these algorithms for customer enablement and empowerment are discussed: e.g. the detection of low-level cluster structures from retail purchase data, the analysis of the co-usage structure of scientific documents for detecting multilevel category structures for scientific libraries, and the analysis of social groups from the friend relation of social network sites.