Polynomial algorithms for nested univariate clustering

Authors:
Pierre Hansen;Brigitte Jaumard;Bruno Simeone
Affiliations:
GERAD and École des Hautes Études Commerciales, Ecole Polytechnique Montréal, 5255 Ave. Decelles Montreal, Quebec, Canada;GERAD and École Polytechnique de Montréal, 5255 Ave. Decelles Montreal, Quebec, Canada;Department of Statistics, University "La Sapienza", Rome, Italy
Venue:
Discrete Mathematics
Year:
2002

Citing 5
Cited 1

On clustering problems with connected optima in Euclidean spaces

Discrete Mathematics
Most uniform path partitioning and its use in image processing

Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Cluster analysis and mathematical programming

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Randomized sorting in O(n log log n) time and linear space using addition, shift, and bit-wise boolean operations

SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Clustering Algorithms

Clustering Algorithms

A network flow model for clustering segments and minimizing total maintenance and rehabilitation cost

Computers and Industrial Engineering

Quantified Score

Hi-index	0.05

Visualization

Abstract

Clique partitioning in Euclidean space Rn consists in finding a partition of a given set of N points into M clusters in order to minimize the sum of within-cluster interpoint distances. For n = 1 clusters need not consist of consecutive points on a line but have a nestedness property. Exploiting this property, an O(N5M2) dynamic programming algorithm is proposed. A θ(N) algorithm is also given for the case M = 2.