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Significantly distinct branches of hierarchical trees: A framework for statistical analysis and applications to biological data

Guoli Sun, Alexander Krasnitz
doi: https://doi.org/10.1101/002188
Guoli Sun
1Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, USA
2Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA
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Alexander Krasnitz
1Simons Center for Quantitative Biology, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY 11724, USA
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  • For correspondence: gsun@cshl.edu krasnitz@cshl.edu
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Abstract

Background One of the most common goals of hierarchical clustering is finding those branches of a tree that form quantifiably distinct data subtypes. Achieving this goal in a statistically meaningful way requires (a) a measure of distinctness of a branch and (b) a test to determine the significance of the observed measure, applicable to all branches and across multiple scales of dissimilarity.

Results We formulate a method termed Tree Branches Evaluated Statistically for Tightness (TBEST) for identifying significantly distinct tree branches in hierarchical clusters. For each branch of the tree a measure of distinctness, or tightness, is defined as a rational function of heights, both of the branch and of its parent. A statistical procedure is then developed to determine the significance of the observed values of tightness. We test TBEST as a tool for tree-based data partitioning by applying it to five benchmark datasets, one of them synthetic and the other four each from a different area of biology. For each dataset there is a well-defined partition of the data into classes. In all test cases TBEST performs on par with or better than the existing techniques.

Conclusions Based on our benchmark analysis, TBEST is a tool of choice for detection of significantly distinct branches in hierarchical trees grown from biological data. An R language implementation of the method is available from the Comprehensive R Archive Network: cran.r-project.org/web/packages/TBEST/index.html.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted June 05, 2014.
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Significantly distinct branches of hierarchical trees: A framework for statistical analysis and applications to biological data
Guoli Sun, Alexander Krasnitz
bioRxiv 002188; doi: https://doi.org/10.1101/002188
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Significantly distinct branches of hierarchical trees: A framework for statistical analysis and applications to biological data
Guoli Sun, Alexander Krasnitz
bioRxiv 002188; doi: https://doi.org/10.1101/002188

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