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New models for symbolic data analysis

Author

Listed:
  • Boris Beranger

    (UNSW Data Science Hub (uDASH), University of New South Wales)

  • Huan Lin

    (UNSW Data Science Hub (uDASH), University of New South Wales)

  • Scott Sisson

    (UNSW Data Science Hub (uDASH), University of New South Wales)

Abstract

Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is required at this level. Here we consider a different perspective, which opens a new research direction in the field of SDA. We assume that, as with a standard statistical analysis, inference is required at the level of individual-level data. However, the individual-level data are unobserved, and are aggregated into observed symbols—group-based distributional-valued summaries—prior to the analysis. We introduce a novel general method for constructing likelihood functions for symbolic data based on a desired probability model for the underlying measurement-level data, while only observing the distributional summaries. This approach opens the door for new classes of symbol design and construction, in addition to developing SDA as a viable tool to enable and improve upon classical data analyses, particularly for very large and complex datasets. We illustrate this new direction for SDA research through several real and simulated data analyses, including a study of novel classes of multivariate symbol construction techniques.

Suggested Citation

  • Boris Beranger & Huan Lin & Scott Sisson, 2023. "New models for symbolic data analysis," 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(3), pages 659-699, September.
    • Handle: RePEc:spr:advdac:v:17:y:2023:i:3:d:10.1007_s11634-022-00520-8
    DOI: 10.1007/s11634-022-00520-8
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    References listed on IDEAS

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