| | |
| | |
Stat |
Members: 3645 Articles: 2'504'928 Articles rated: 2609
25 April 2024 |
|
| | | |
|
Article overview
| |
|
How many clusters? An information theoretic perspective | Susanne Still
; William Bialek
; | Date: |
4 Mar 2003 | Subject: | Data Analysis, Statistics and Probability; General Physics | physics.data-an physics.gen-ph | 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 either on 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 which arises due to sampling errors will allow us to find a clustering solution at a temperature which 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 which can be resolved from the data in the hard clustering limit. | Source: | arXiv, physics/0303011 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |