title: K-ary clustering with optimal leaf ordering for gene expression data.
abstract: BACKGROUND
  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.
  
  
  RESULTS
  We present an algorithm that efficiently 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 and missing values. By optimally ordering the leaves of the resulting tree we maintain the pairwise relationships that appear in the original method, without sacrificing the robustness. Our k-ary construction algorithm runs in O(n(3)) regardless of k and our ordering algorithm runs in O(4(k)n(3)). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results in both global presentation and cluster identification.
  
  
  BACKGROUND
  We have implemented the above algorithms in C++ on the Linux operating system.
authors.affiliation: Laboratory for Computer Science, MIT, 545 Technology Square, Cambridge, MA 02139, USA. zivbj@mit.edu
authors.forename: Ziv
authors.initials: Z
authors.lastname: Bar-Joseph
authors.forename: Erik D
authors.initials: ED
authors.lastname: Demaine
authors.forename: David K
authors.initials: DK
authors.lastname: Gifford
authors.forename: Nathan
authors.initials: N
authors.lastname: Srebro
authors.forename: Angèle M
authors.initials: AM
authors.lastname: Hamel
authors.forename: Tommi S
authors.initials: TS
authors.lastname: Jaakkola
mesh_terms: D000465:Algorithms; D000818:Animals; D002060:Bursa of Fabricius / Q000473:pathology; D002645:Chickens; D016000:Cluster Analysis; D003663:Decision Trees; D020869:Gene Expression Profiling / Q000379:methods*; D015972:Gene Expression Regulation, Neoplastic / Q000235:genetics; D016259:Genes, myc / Q000235:genetics; D016393:Lymphoma, B-Cell / Q000235:genetics; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods; D010363:Pattern Recognition, Automated; D011786:Quality Control; D016415:Sequence Alignment; D017422:Sequence Analysis, DNA / Q000379:methods*; D017385:Sequence Homology; D013269:Stochastic Processes; D014584:User-Computer Interface