### Abstract

In the cluster analysis problem one seeks to partition a finite set of objects into disjoint groups (or clusters) such that each group contains relatively similar objects and, relatively dissimilar objects are placed in different groups. For certain classes of the problem or, under certain assumptions, the partitioning exercise can be formulated as a sequence of linear programs (LPs), each with a parametric objective function. Such LPs can be solved using the parametric linear programming procedure developed by Gass and Saaty [(Gass, S., Saaty, T. (1955), Naval Research Logistics Quarterly 2, 39-45)]. In this paper, a parametric linear programming model for solving cluster analysis problems is presented. We show how this model can be used to find optimal solutions for certain variations of the clustering problem or, in other cases, for an approximation of the general clustering problem.

Original language | English (US) |
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Pages (from-to) | 582-588 |

Number of pages | 7 |

Journal | European Journal of Operational Research |

Volume | 111 |

Issue number | 3 |

DOIs | |

State | Published - Dec 16 1998 |

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### Keywords

- Clustering
- Integer programming
- Lagrangian relaxation
- Parametric linear programming

### ASJC Scopus subject areas

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research
- Information Systems and Management

### Cite this

*European Journal of Operational Research*,

*111*(3), 582-588. https://doi.org/10.1016/S0377-2217(97)00379-2