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Statistical Archetypal Analysis for Cognitive Categorization

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New Statistical Developments in Data Science (SIS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 288))

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Abstract

Human knowledge develops through complex relationships between categories. In the era of Big Data, the concept of categorization implies data summarization in a limited number of well-separated groups that must be maximally and internally homogeneous at the same time. This proposal exploits archetypal analysis capabilities by finding a set of extreme points that can summarize entire data sets in homogeneous groups. The archetypes are then used to identify the best prototypes according to Rosch’s definition. Finally, in the geometric approach to cognitive science, the Voronoi tessellation based on the prototypes is used to define categorization. An example using a well-known wine dataset by Forina et al. illustrates the procedure.

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Author information

Authors and Affiliations

  1. Dept. of Social Sciences, Università degli Studi di Napoli Federico II, Naples, Italy

    Francesco Santelli

  2. Dept. of Political Sciences, Università degli Studi di Napoli Federico II, Naples, Italy

    Francesco Palumbo & Giancarlo Ragozini

Authors
  1. Francesco Santelli
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  2. Francesco Palumbo
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  3. Giancarlo Ragozini
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Corresponding author

Correspondence to Francesco Palumbo .

Editor information

Editors and Affiliations

  1. Dipartimento di Statistica, Informatica, Applicazioni ‘G. Parenti’ (DiSIA), Università degli Studi di Firenze, Florence, Italy

    Alessandra Petrucci

  2. Dipartimento Scienze Statistiche, Sapienza Università di Roma, Rome, Italy

    Filomena Racioppi

  3. Dipartimento di Matematica e Fisica, Università della Campania ‘Luigi Vanvitelli’, Caserta, Italy

    Rosanna Verde

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Santelli, F., Palumbo, F., Ragozini, G. (2019). Statistical Archetypal Analysis for Cognitive Categorization. In: Petrucci, A., Racioppi, F., Verde, R. (eds) New Statistical Developments in Data Science. SIS 2017. Springer Proceedings in Mathematics & Statistics, vol 288. Springer, Cham. https://doi.org/10.1007/978-3-030-21158-5_7

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