### Abstract

Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate for the description of a given system. Traditional approaches to this problem are based on either a framework in which clusters of a particular shape are assumed as a model of the system or on a two-step procedure in which a clustering criterion determines the optimal assignments for a given number of clusters and a separate criterion measures the goodness of the classification to determine the number of clusters. In a statistical mechanics approach, clustering can be seen as a trade-off between energy- and entropy-like terms, with lower temperature driving the proliferation of clusters to provide a more detailed description of the data. For finite data sets, we expect that there is a limit to the meaningful structure that can be resolved and therefore a minimum temperature beyond which we will capture sampling noise. This suggests that correcting the clustering criterion for the bias that arises due to sampling errors will allow us to find a clustering solution at a temperature that is optimal in the sense that we capture maximal meaningful structure-without having to define an external criterion for the goodness or stability of the clustering. We show that in a general information-theoretic framework, the finite size of a data set determines an optimal temperature, and we introduce a method for finding the maximal number of clusters that can be resolved from the data in the hard clustering limit.

Original language | English (US) |
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Pages (from-to) | 2483-2506 |

Number of pages | 24 |

Journal | Neural computation |

Volume | 16 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2004 |

### All Science Journal Classification (ASJC) codes

- Arts and Humanities (miscellaneous)
- Cognitive Neuroscience

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## Cite this

*Neural computation*,

*16*(12), 2483-2506. https://doi.org/10.1162/0899766042321751