Group Factor Analysis
This work addresses the need for analyzing high-dimensional data sources in life sciences, such as brain activation and systems biology, by providing a more flexible and accurate group factor analysis method, though it appears incremental as an extension of classical techniques.
The authors tackled the problem of extending factor analysis to model relationships between groups of variables, introducing a method that also generalizes canonical correlation analysis to more than two sets. They demonstrated that their solution outperforms alternative factor analysis-based methods, showing its applicability on brain activation and systems biology data sets.
Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each group represents either a set of related variables or a data set. The model also naturally extends canonical correlation analysis to more than two sets, in a way that is more flexible than previous extensions. Our solution is formulated as variational inference of a latent variable model with structural sparsity, and it consists of two hierarchical levels: The higher level models the relationships between the groups, whereas the lower models the observed variables given the higher level. We show that the resulting solution solves the group factor analysis problem accurately, outperforming alternative factor analysis based solutions as well as more straightforward implementations of group factor analysis. The method is demonstrated on two life science data sets, one on brain activation and the other on systems biology, illustrating its applicability to the analysis of different types of high-dimensional data sources.