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 withother related ones show its effectiveness on randomly generated benchmark problems and hard synthetic data sets

Keywords:

Clustering , optimization problem , nonnegative orthogonal constraints