Two-way analysis of high-dimensional collinear data |
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Authors: | Ilkka Huopaniemi Tommi Suvitaival Janne Nikkilä Matej Orešič Samuel Kaski |
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Affiliation: | (1) Department of Information and Computer Science, Helsinki University of Technology (TKK), P.O. Box 5400, 02015 Espoo, Finland;(2) Department of Basic Veterinary Sciences (Division of Microbiology and Epidemiology), Faculty of Veterinary Medicine, University of Helsinki, P.O. Box 66, 00014 Helsinki, Finland;(3) VTT Technical Research Centre of Finland (VTT), P.O. Box 1000, 02044 Espoo, Finland |
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Abstract: | We present a Bayesian model for two-way ANOVA-type analysis of high-dimensional, small sample-size datasets with highly correlated
groups of variables. Modern cellular measurement methods are a main application area; typically the task is differential analysis
between diseased and healthy samples, complicated by additional covariates requiring a multi-way analysis. The main complication
is the combination of high dimensionality and low sample size, which renders classical multivariate techniques useless. We
introduce a hierarchical model which does dimensionality reduction by assuming that the input variables come in similarly-behaving
groups, and performs an ANOVA-type decomposition for the set of reduced-dimensional latent variables. We apply the methods
to study lipidomic profiles of a recent large-cohort human diabetes study. |
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Keywords: | ANOVA Factor analysis Hierarchical model Metabolomics Multi-way analysis Small sample-size |
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