# Bayesian Group Factor Analysis

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Seppo Virtanen,
Arto Klami,
Suleiman Khan,
Samuel Kaski
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Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1269-1277, 2012.

#### Abstract

We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternative variables collected from statistics tables to measure one property of interest. We show that by assuming group-wise sparse factors, active in a subset of the sets, the variation can be decomposed into factors explaining relationships between the sets and factors explaining away set-specific variation. We formulate the assumptions in a Bayesian model providing the factors, and apply the model to two data analysis tasks, in neuroimaging and chemical systems biology.

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