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**Optimization based DC programming and DCA for hierarchical clustering.**
*(English)*
Zbl 1149.90117

A hierarchical clustering of a set of objects can be described as a tree, in which the leaves are precisely the objects to be clustered. In this work different mathematical programs have been proposed for the bilevel hierarchical clustering problem. The proposed approach is based on DC (Difference of Convex functions) programming “which deals with DC programs, i.e., the minimization of a DC function over a convex set” and DC optimization Algorithm called DCA. They are all nonconvex, nonsmooth optimization problems that can be reformulated as DC programs in a suitable matrix space for which the resulting DCA schemes are all explicit, and very inexpensive. Numerical results on some artificial and real-world databases demonstrate that the proposed algorithms are more efficient than some existing optimization based clustering algorithms.

Reviewer: Samir Kumar Neogy (New Delhi)

### MSC:

90C26 | Nonconvex programming, global optimization |

### Keywords:

bilevel hierarchical clustering; DC programming; DCA; nonsmooth optimization; nonconvex programs
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\textit{Le Thi Hoai An} et al., Eur. J. Oper. Res. 183, No. 3, 1067--1085 (2007; Zbl 1149.90117)

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### References:

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