# The cluster structure function

arXiv: https://arxiv.org/abs/2201.01222 · HTML: https://mlsanity.com/paper/2201.01222/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 48 references that are in the map.
- First posted on arXiv 4 Jan 2022.

## Builds on (most cited first, 4 of 4)

- [Bayesian cluster analysis: Point estimation and credible balls](https://mlsanity.com/paper/1505.03339/) (2015)
- [Estimating the number of clusters using cross-validation](https://mlsanity.com/paper/1702.02658/) (2017)
- [Bayesian Cluster Enumeration Criterion for Unsupervised Learning](https://mlsanity.com/paper/1710.07954/) (2017)
- [Algorithmic statistics, prediction and machine learning](https://mlsanity.com/paper/1509.05473/) (2015)

## Built on by (most cited first, 2 of 2)

- [A Kolmogorov metric embedding for live cell microscopy signaling patterns](https://mlsanity.com/paper/2401.02501/) (2024)
- [Algorithmic statistics of retinal images](https://mlsanity.com/paper/2608.09989/) (2026)

## Abstract (arXiv)

For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every number between one and the number of data, the result is a function, the cluster structure function. It maps the number of parts of a partition to values related to the deficiencies of being good models by the parts. Such a function starts with a value at least zero for no partition of the data set and descents to zero for the partition of the data set into singleton parts. The optimal clustering is the one chosen to minimize the cluster structure function. The theory behind the method is expressed in algorithmic information theory (Kolmogorov complexity). In practice the Kolmogorov complexities involved are approximated by a concrete compressor. We give examples using real data sets: the MNIST handwritten digits and the segmentation of real cells as used in stem cell research.