Tam sayılı karma programlama ile kümeleme probleminin modellenmesi ve bir müşteri segmentasyonu uygulaması

Clustering is an important data mining problem that identifies groups of entities thatare similar to each other with respect to a certain number of attributes. In this thesis, twomathematical programming based approaches to clustering are presented. The proposedmathematical programming based approaches are applied to a digital platform company?scustomer segmentation problem involving transactional attributes related to thecustomers. In the first model, the clustering problem is formulated as a mixed-integerlinear programming problem with the objective of minimizing the maximum clusterdiameter among all clusters. In order to overcome difficulties related to computationalcomplexity of this model, a heuristic clustering approach is developed that improvescomputational times dramatically without compromising from optimality in most of thecases that were tested. In the second model, the clustering problem is modeled as amixed-integer nonlinear programming problem with the objective of minimization of sumof within-group distances. We show that every extreme point solution of the nonlinearrelaxation of the model is integer due to the unimodularity property of the constraint setof the model. We solve the continuous relaxation of the model, obtain integer solutionsand observe that solution time of the model is very short. Although the model is solved tolocal optimality, the interpretations derived from the solution of the model are promising.The performance of the approaches is tested both on an illustrative example and on a realproblem. The analysis of the results indicates that the approaches are computationallyefficient and create meaningful segmentation of data.Advisor: Metin Türkay Date: July 21, 2005Director: Yaman Arkun Date: July 21, 2005