TY - GEN

T1 - Interval finding and its application to data mining

AU - Fukuda, Takeshi

AU - Morimoto, Yasuhiko

AU - Morishita, Shinich

AU - Tokuyama, Takeshi

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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={0, 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 algorithms 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 f(I) = Σi ∈ I f(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.

AB - 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={0, 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 algorithms 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 f(I) = Σi ∈ I f(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.

UR - http://www.scopus.com/inward/record.url?scp=84990203846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990203846&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84990203846

SN - 3540620486

SN - 9783540620488

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 55

EP - 64

BT - Algorithms and Computation - 7th International Symposium, ISAAC 1996, Proceedings

A2 - Nagamochi, Hiroshi

A2 - Miyano, Satoru

A2 - Asano, Tetsuo

A2 - Igarashi, Yoshihide

A2 - Suri, Subhash

PB - Springer-Verlag

T2 - 7th International Symposium on Algorithms and Computation, ISAAC 1996

Y2 - 16 December 1996 through 18 December 1996

ER -