title: Model-based clustering with certainty estimation: implication for clade assignment of influenza viruses.
abstract: BACKGROUND
  Clustering is a common technique used by molecular biologists to group homologous sequences and study evolution. There remain issues such as how to cluster molecular sequences accurately and in particular how to evaluate the certainty of clustering results.
  
  
  RESULTS
  We presented a model-based clustering method to analyze molecular sequences, described a subset bootstrap scheme to evaluate a certainty of the clusters, and showed an intuitive way using 3D visualization to examine clusters. We applied the above approach to analyze influenza viral hemagglutinin (HA) sequences. Nine clusters were estimated for high pathogenic H5N1 avian influenza, which agree with previous findings. The certainty for a given sequence that can be correctly assigned to a cluster was all 1.0 whereas the certainty for a given cluster was also very high (0.92-1.0), with an overall clustering certainty of 0.95. For influenza A H7 viruses, ten HA clusters were estimated and the vast majority of sequences could be assigned to a cluster with a certainty of more than 0.99. The certainties for clusters, however, varied from 0.40 to 0.98; such certainty variation is likely attributed to the heterogeneity of sequence data in different clusters. In both cases, the certainty values estimated using the subset bootstrap method are all higher than those calculated based upon the standard bootstrap method, suggesting our bootstrap scheme is applicable for the estimation of clustering certainty.
  
  
  CONCLUSIONS
  We formulated a clustering analysis approach with the estimation of certainties and 3D visualization of sequence data. We analysed 2 sets of influenza A HA sequences and the results indicate our approach was applicable for clustering analysis of influenza viral sequences.
authors.affiliation: Department of Statistics, University of Central Florida, Orlando, FL, 32816, USA. shunpu.zhang@ucf.edu.
authors.forename: Shunpu
authors.initials: S
authors.lastname: Zhang
authors.affiliation: College of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China.
authors.forename: Zhong
authors.initials: Z
authors.lastname: Li
authors.affiliation: Department of Biology, University of Nebraska at Omaha, Omaha, NE, 68182, USA.
authors.forename: Kevin
authors.initials: K
authors.lastname: Beland
authors.affiliation: Department of Biology, University of Nebraska at Omaha, Omaha, NE, 68182, USA. glu3@unomaha.edu.
authors.forename: Guoqing
authors.identifier: http://orcid.org/0000-0002-2728-9604
authors.initials: G
authors.lastname: Lu
mesh_terms: D000818:Animals; D001483:Base Sequence; D001717:Birds; D016000:Cluster Analysis; D006389:Hemagglutinins, Viral / Q000737:chemistry; D053124:Influenza A Virus, H5N1 Subtype / Q000145:classification* / Q000378:metabolism; D005585:Influenza in Birds / Q000821:virology; D008962:Models, Theoretical; D010802:Phylogeny
chemical_list: D006389:Hemagglutinins, Viral
keywords: Bootstrap; Certainty; Influenza A hemagglutinin (HA); Model-based clustering; Multidimensional scaling