Clustering is widely studied in data mining community. It is used to partition data set into clusters so that intra-cluster data are similar and inter-cluster data are dissimilar. Different clustering methods use different similarity definition and techniques. Several popular clustering algorithms are analyzed from three different viewpoints: (1) clustering criteria, (2) cluster representation, and (3) algorithm framework. Furthermore, some new built algorithms, which mix or generalize some other algorithms, are introduced. Since the analysis is from several viewpoints, it can cover and distinguish most of the existing algorithms. It is the basis of the research of self-tuning algorithm and clustering benchmark.