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Clusters of high-dimensional interval data and related Boolean functions of events in Euclidean space.

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Title: Clusters of high-dimensional interval data and related Boolean functions of events in Euclidean space.
Authors: Lee, Jinwook1 (AUTHOR) jl3539@drexel.edu, Prékopa, András2 (AUTHOR)
Source: Annals of Operations Research. Nov2025, Vol. 354 Issue 3, p1179-1197. 19p.
Subjects: Clustering algorithms, Boolean functions, Metric spaces, Polynomial time algorithms, Metadata
Abstract: Clustering interval data has been studied for decades. High-dimensional interval data can be expressed in terms of hyperrectangles in R d (or d-orthotopes) in case of real-valued d-attributes data. This paper investigates such high-dimensional interval data: the Cartesian product of intervals, or a vector of interval. For the efficient computation of related Boolean functions, some interesting aspects have been discovered using vertices and edges of the graph, generated from given events. We also study the lower and upper-bounded orthants in R d as events for which we show the existence of a polynomial-time algorithm to calculate the probability of the union of such events. This efficient algorithm has been discovered by constructing a suitable partial order relation based on a recursive projection onto lower-dimensional spaces. Illustrative real-life applications are presented. [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Clusters of high-dimensional interval data and related Boolean functions of events in Euclidean space.
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  Data: <searchLink fieldCode="JN" term="%22Annals+of+Operations+Research%22">Annals of Operations Research</searchLink>. Nov2025, Vol. 354 Issue 3, p1179-1197. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Clustering+algorithms%22">Clustering algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+functions%22">Boolean functions</searchLink><br /><searchLink fieldCode="DE" term="%22Metric+spaces%22">Metric spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomial+time+algorithms%22">Polynomial time algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Metadata%22">Metadata</searchLink>
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  Data: Clustering interval data has been studied for decades. High-dimensional interval data can be expressed in terms of hyperrectangles in R d (or d-orthotopes) in case of real-valued d-attributes data. This paper investigates such high-dimensional interval data: the Cartesian product of intervals, or a vector of interval. For the efficient computation of related Boolean functions, some interesting aspects have been discovered using vertices and edges of the graph, generated from given events. We also study the lower and upper-bounded orthants in R d as events for which we show the existence of a polynomial-time algorithm to calculate the probability of the union of such events. This efficient algorithm has been discovered by constructing a suitable partial order relation based on a recursive projection onto lower-dimensional spaces. Illustrative real-life applications are presented. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10479-021-03951-2
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        Text: English
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      – SubjectFull: Boolean functions
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      – SubjectFull: Metric spaces
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      – SubjectFull: Polynomial time algorithms
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      – SubjectFull: Metadata
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              Text: Nov2025
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