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Internet security applications of Grobner-Shirvov bases

- Kelarev, Andrei, Yearwood, John, Watters, Paul

**Authors:**Kelarev, Andrei , Yearwood, John , Watters, Paul**Date:**2010**Type:**Text , Journal article**Relation:**Asian-European Journal of Mathematics Vol. 3, no. 3 (2010), p. 435-442**Relation:**http://purl.org/au-research/grants/arc/DP0211866**Full Text:**false**Reviewed:**

A heuristic algorithm for solving the minimum sum-of-squares clustering problems

**Authors:**Ordin, Burak , Bagirov, Adil**Date:**2015**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 61, no. 2 (2015), p. 341-361**Relation:**http://purl.org/au-research/grants/arc/DP140103213**Full Text:**false**Reviewed:****Description:**Clustering is an important task in data mining. It can be formulated as a global optimization problem which is challenging for existing global optimization techniques even in medium size data sets. Various heuristics were developed to solve the clustering problem. The global k-means and modified global k-means are among most efficient heuristics for solving the minimum sum-of-squares clustering problem. However, these algorithms are not always accurate in finding global or near global solutions to the clustering problem. In this paper, we introduce a new algorithm to improve the accuracy of the modified global k-means algorithm in finding global solutions. We use an auxiliary cluster problem to generate a set of initial points and apply the k-means algorithm starting from these points to find the global solution to the clustering problems. Numerical results on 16 real-world data sets clearly demonstrate the superiority of the proposed algorithm over the global and modified global k-means algorithms in finding global solutions to clustering problems.

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