## Definition

Partitional clustering decomposes a data set into a set of disjoint clusters. Given a data set of *N* points, a partitioning method constructs *K* (*N* ≥ *K*) 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

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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## Recommended Reading

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. https://doi.org/10.1007/978-0-387-30164-8_631

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