Erratum: the Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Fast hierarchical clustering and other applications of dynamic closest pairs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic hierarchical clustering for biological data
Proceedings of the sixth annual international conference on Computational biology
Parameterized Complexity
Approximation algorithms for hierarchical location problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Dendrogram seriation using simulated annealing
Information Visualization
Approximation algorithms for hierarchical location problems
Journal of Computer and System Sciences - Special issue on network algorithms 2005
Visual triangulation of network-based phylogenetic trees
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
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A major challenge in gene expression analysis is effective data organization and visualization. One of the most popular tools for this task is hierarchical clustering. Hierarchical clustering allows a user to view relationships in scales ranging from single genes to large sets of genes, while at the same time providing a global view of the expression data. However, hierarchical clustering is very sensitive to noise, it usually lacks of a method to actually identify distinct clusters, and produces a large number of possible leaf orderings of the hierarchical clustering tree. In this paper we propose a new hierarchical clustering algorithm which reduces susceptibility to noise, permits up to k siblings to be directly related, and provides a single optimal order for the resulting tree. Our algorithm constructs a k-ary tree, where each node can have up to k children, and then optimally orders the leaves of that tree. By combining k clusters at each step our algorithm becomes more robust against noise. By optimally ordering the leaves of the tree we maintain the pairwise relationships that appear in the original method. Our k-ary construction algorithm runs in O(n3) regardless of k and our ordering algorithm runs in O(4k+o(k)n3). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results.