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Interpreting clusters via prototype optimization

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  • Carrizosa, Emilio
  • Kurishchenko, Kseniia
  • Marín, Alfredo
  • Romero Morales, Dolores

Abstract

In this paper, we tackle the problem of enhancing the interpretability of the results of Cluster Analysis. Our goal is to find an explanation for each cluster, such that clusters are characterized as precisely and distinctively as possible, i.e., the explanation is fulfilled by as many as possible individuals of the corresponding cluster, true positive cases, and by as few as possible individuals in the remaining clusters, false positive cases. We assume that a dissimilarity between the individuals is given, and propose distance-based explanations, namely those defined by individuals that are close to its so-called prototype. To find the set of prototypes, we address the biobjective optimization problem that maximizes the total number of true positive cases across all clusters and minimizes the total number of false positive cases, while controlling the true positive rate as well as the false positive rate in each cluster. We develop two mathematical optimization models, inspired by classic Location Analysis problems, that differ in the way individuals are allocated to prototypes. We illustrate the explanations provided by these models and their accuracy in both real-life data as well as simulated data.

Suggested Citation

  • Carrizosa, Emilio & Kurishchenko, Kseniia & Marín, Alfredo & Romero Morales, Dolores, 2022. "Interpreting clusters via prototype optimization," Omega, Elsevier, vol. 107(C).
    • Handle: RePEc:eee:jomega:v:107:y:2022:i:c:s0305048321001523
    DOI: 10.1016/j.omega.2021.102543
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    References listed on IDEAS

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    1. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    2. Emilio Carrizosa & Belén Martín-Barragán & Frank Plastria & Dolores Romero Morales, 2007. "On the Selection of the Globally Optimal Prototype Subset for Nearest-Neighbor Classification," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 470-479, August.
    3. Benítez-Peña, Sandra & Bogetoft, Peter & Romero Morales, Dolores, 2020. "Feature Selection in Data Envelopment Analysis: A Mathematical Optimization approach," Omega, Elsevier, vol. 96(C).
    4. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    5. Onur Seref & Ya-Ju Fan & Wanpracha Art Chaovalitwongse, 2014. "Mathematical Programming Formulations and Algorithms for Discrete k-Median Clustering of Time-Series Data," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 160-172, February.
    6. Bart Baesens & Rudy Setiono & Christophe Mues & Jan Vanthienen, 2003. "Using Neural Network Rule Extraction and Decision Tables for Credit-Risk Evaluation," Management Science, INFORMS, vol. 49(3), pages 312-329, March.
    7. Jon Kleinberg & Himabindu Lakkaraju & Jure Leskovec & Jens Ludwig & Sendhil Mullainathan, 2018. "Human Decisions and Machine Predictions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(1), pages 237-293.
    8. Carrizosa, Emilio & Nogales-Gómez, Amaya & Romero Morales, Dolores, 2017. "Clustering categories in support vector machines," Omega, Elsevier, vol. 66(PA), pages 28-37.
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    Cited by:

    1. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    2. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 407-429, June.

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