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Algorithms of maximum likelihood data clustering with applications

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  • Giada, Lorenzo
  • Marsili, Matteo

Abstract

We address the problem of data clustering by introducing an unsupervised, parameter-free approach based on maximum likelihood principle. Starting from the observation that data sets belonging to the same cluster share a common information, we construct an expression for the likelihood of any possible cluster structure. The likelihood in turn depends only on the Pearson's coefficient of the data. We discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations. Compared to standard clustering methods, our approach has the advantages that (i) it is parameter free, (ii) the number of clusters need not be fixed in advance and (iii) the interpretation of the results is transparent. In order to test our approach and compare it with standard clustering algorithms, we analyze two very different data sets: time series of financial market returns and gene expression data. We find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability.

Suggested Citation

  • Giada, Lorenzo & Marsili, Matteo, 2002. "Algorithms of maximum likelihood data clustering with applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 650-664.
    • Handle: RePEc:eee:phsmap:v:315:y:2002:i:3:p:650-664
    DOI: 10.1016/S0378-4371(02)00974-3
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    Citations

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    Cited by:

    1. khoojine, Arash Sioofy & Han, Dong, 2019. "Network analysis of the Chinese stock market during the turbulence of 2015–2016 using log-returns, volumes and mutual information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1091-1109.
    2. Zhang, Ningning & Lin, Aijing & Yang, Pengbo, 2020. "Detrended moving average partial cross-correlation analysis on financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Dieter Hendricks & Diane Wilcox & Tim Gebbie, 2014. "High-speed detection of emergent market clustering via an unsupervised parallel genetic algorithm," Papers 1403.4099, arXiv.org, revised Aug 2015.
    4. Marc Bailly-Bechet & Antoine Danchin & Mudassar Iqbal & Matteo Marsili & Massimo Vergassola, 2006. "Codon Usage Domains over Bacterial Chromosomes," PLOS Computational Biology, Public Library of Science, vol. 2(4), pages 1-13, April.
    5. Schäfer, Rudi & Guhr, Thomas, 2010. "Local normalization: Uncovering correlations in non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3856-3865.
    6. Andreas Muhlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Papers 1803.00261, arXiv.org.
    7. Yelibi, Lionel & Gebbie, Tim, 2020. "Fast Super-Paramagnetic Clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    8. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    9. Musciotto, F. & Marotta, L. & Miccichè, S. & Mantegna, R.N., 2018. "Bootstrap validation of links of a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1032-1043.
    10. Dieter Hendricks, 2016. "Using real-time cluster configurations of streaming asynchronous features as online state descriptors in financial markets," Papers 1603.06805, arXiv.org, revised May 2017.
    11. Arash Sioofy Khoojine & Mahboubeh Shadabfar & Yousef Edrisi Tabriz, 2022. "A Mutual Information-Based Network Autoregressive Model for Crude Oil Price Forecasting Using Open-High-Low-Close Prices," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
    12. Rudi Schafer & Nils Fredrik Nilsson & Thomas Guhr, 2010. "Power mapping with dynamical adjustment for improved portfolio optimization," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 107-119.
    13. Shi, Wenbin & Shang, Pengjian & Wang, Jing & Lin, Aijing, 2014. "Multiscale multifractal detrended cross-correlation analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 35-44.
    14. Shi, Wenbin & Shang, Pengjian & Xia, Jianan & Yeh, Chien-Hung, 2016. "The coupling analysis between stock market indices based on permutation measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 222-231.
    15. Andreas Mühlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Risks, MDPI, vol. 6(2), pages 1-25, April.
    16. Mao, Xuegeng & Shang, Pengjian, 2018. "Extended AIC model based on high order moments and its application in the financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 264-275.

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