Clustering as an Example of Optimizing Arbitrarily Chosen Objective Functions

This paper is a reflection upon a common practice of solving various types of learning problems by optimizing arbitrarily chosen criteria in the hope that they are well correlated with the criterion actually used for assessment of the results. This issue has been investigated using clustering as an example, hence a unified view of clustering as an optimization problem is first proposed, stemming from the belief that typical design choices in clustering, like the number of clusters or similarity measure can be, and often are suboptimal, also from the point of view of clustering quality measures later used for algorithm comparison and ranking. In order to illustrate our point we propose a generalized clustering framework and provide a proof-of-concept using standard benchmark datasets and two popular clustering methods for comparison.