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The Lookup Table Regression Model for Histogram-Valued Symbolic Data

Author

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  • Manabu Ichino

    (School of Science and Engineering, Tokyo Denki University, Hatoyama, Saitama 350-0394, Japan)

Abstract

This paper presents the Lookup Table Regression Model (LTRM) for histogram-valued symbolic data. We first transform the given symbolic data to a numerical data table by the quantile method. Then, under the selected response variable, we apply the Monotone Blocks Segmentation (MBS) to the obtained numerical data table. If the selected response variable and some remained explanatory variable(s) organize a monotone structure, the MBS generates a Lookup Table composed of interval values. For a given object, we search the nearest value of an explanatory variable, then the corresponding value of the response variable becomes the estimated value. If the response variable and the explanatory variable(s) are covariate but they follow to a non-monotonic structure, we need to divide the given data into several monotone substructures. For this purpose, we apply the hierarchical conceptual clustering to the given data, and we obtain Multiple Lookup Tables by applying the MBS to each of substructures. We show the usefulness of the proposed method by using an artificial data set and real data sets.

Suggested Citation

  • Manabu Ichino, 2022. "The Lookup Table Regression Model for Histogram-Valued Symbolic Data," Stats, MDPI, vol. 5(4), pages 1-23, December.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:77-1293:d:993161
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    References listed on IDEAS

    as
    1. Antonio Irpino & Rosanna Verde, 2015. "Linear regression for numeric symbolic variables: a least squares approach based on Wasserstein Distance," 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. 9(1), pages 81-106, March.
    2. Manabu Ichino & Kadri Umbleja & Hiroyuki Yaguchi, 2021. "Unsupervised Feature Selection for Histogram-Valued Symbolic Data Using Hierarchical Conceptual Clustering," Stats, MDPI, vol. 4(2), pages 1-26, May.
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