Clustering: An Optimization Approach

Partitioning a given data set into subsets based on similarity among the data ‎is called clustering‎. Clustering is a major task in data mining and machine learning with many applications such as text retrieval, pattern recognition and web mining. Here, we briefly review some clustering ‎problems (k-means, normalized k-cut and isoperimetry) ‎and describe ‎their ‎connections. ‎W‎e show that the relaxed mean version of the isoperimetry problem is formulated as an optimization problem with nonnegative orthogonal constraints. Using the algorithm proposed by Wen and Yin to solve this kind of a problem, we extract a solution of the clustering problem. A comparative performance analysis of our approach with other related ones show its effectiveness on randomly generated benchmark problems and hard synthetic data sets.