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ExPlanes: Exploring Planes in Triplet Data
Schwenk, Bruno B. ; Selbig, Joachim ; Ben-Zion, Yehuda ; Holschneider, Matthias
Journal of Integrative Bioinformatics - JIB (ISSN 1613-4516)
Many methods for the analysis of gene expression-, protein- or metabolite-data focus on the investigation of binary relationships, while the underlying biological processes creating this data may generate relations of higher than bivariate complexity. We give a novel method ExPlanes that helps to explore certain types of ternary relationships in a statistically robust, Bayesian framework. To arrive at an characterization of the data structure contained in triplet data we investigate 2-dimensional planes being the only linear structures that cannot be inferred from projections of the data. The key part of our methodology is the definition of a robust, Bayesian plane posterior under the assumption of an invariant prior and a Gaussian error model. A numerical representation of the plane posterior can be explored interactively. Beyond this purely Bayesian approach we can use the plane posterior to construct a family of posterior-based test statistics that allow testing the data for different plane related hypotheses. To demonstrate practicability we queried triplets of metabolic data from a plant crossing experiment for the presence of plane-, line- and point-structures by using posterior-based test statistics and were able to show their distinctiveness.
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ExPlanes: Exploring Planes in Triplet Data.
Journal of Integrative Bioinformatics - JIB (ISSN 1613-4516), 7(3), 2010