Journal article
The Cluster Structure Function
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, v 45(9), p11309
Sep 2023
PMID: 37018105
Abstract
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 selected by analyzing 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.
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Details
- Title
- The Cluster Structure Function
- Publication Details
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, v 45(9), p11309
- Publisher
- IEEE COMPUTER SOC; LOS ALAMITOS
- Grant note
- & nbsp;This work was supported in part by NIH NIA under Grant R01AG041861 and in part by the Human Frontiers Science Program under Grant RGP0043/2019-203.& nbsp;
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:001045832200046
- Scopus ID
- 2-s2.0-85153329675
- Other Identifier
- 991021861301404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Computer Science, Artificial Intelligence
- Engineering, Electrical & Electronic