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Partitional Clustering

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Partitional clustering decomposes a data set into a set of disjoint clusters. Given a data set of N points, a partitioning method constructs K (NK) partitions of the data, with each partition representing a cluster. That is, it classifies the data into K groups by satisfying the following requirements: (1) each group contains at least one point, and (2) each point belongs to exactly one group. Notice that for fuzzy partitioning, a point can belong to more than one group.

Many partitional clustering algorithms try to minimize an objective function. For example, in K-means and K-medoids the function (also referred to as the distortion function) is

$${\sum \limits _{i=1}^{K}}{\sum \limits _{j=1}^{\vert {C}_{i}\vert }}\mathrm{Dist}({x}_{ j},\mathrm{center}(i)),$$

where | C i | is the number of points in cluster i, Dist(x j , center(i)) is the distance between point x j and center i. Many distance functions can be used, such as Euclidean distance and L...

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  • Han, J., & Kamber, M. (2006). Data mining: Concepts and techniques (2nd ed.). San Francisco: Morgan Kaufmann Publishers.

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Jin, X., Han, J. (2011). Partitional Clustering. In: Sammut, C., Webb, G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA.

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