Interval Finding and Its Application to Data Mining

Takeshi FUKUDA  Yasuhiko MORIMOTO  Shinichi MORISHITA  Takeshi TOKUYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.4   pp.620-626
Publication Date: 1997/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
computational geometry,  algorithms,  data mining,  interval searching,  

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In this paper, we investigate inverse problems of the interval query problem in application to data mining. Let I be the set of all intervals on U = {1, 2, , n}. Consider an objective function f(I), conditional functions ui(I) on I, and define an optimization problem of finding the interval I maximizing f(I) subject to ui(I) > Ki for given real numbers Ki (i = 1, 2, , h). We propose efficient alogorithms to solve the above optimization problem if the objective function is either additive or quotient, and the conditional functions are additive, where a function f is additive if f(I) = ΣiIf^(i) extending a function f^ on U, and quotient if it is represented as a quotient of two additive functions. We use computational-geometric methods such as convex hull, range searching, and multidimensional divide-and-conquer.