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Variational Autoencoders (VAEs) provide a flexible and scalable framework fornon-linear dimensionality reduction. However, in application domains such asgenomics where data sets are typically tabular and high-dimensional, ablack-box approach to dimensionality reduction does not provide sufficientinsights. Common data analysis workflows additionally use clustering techniquesto identify groups of similar features. This usually leads to a two-stageprocess, however, it would be desirable to construct a joint modellingframework for simultaneous dimensionality reduction and clustering of features.In this paper, we propose to achieve this through the BasisVAE: a combinationof the VAE and a probabilistic clustering prior, which lets us learn a one-hotbasis function representation as part of the decoder network. Furthermore, forscenarios where not all features are aligned, we develop an extension to handletranslation-invariant basis functions. We show how a collapsed variationalinference scheme leads to scalable and efficient inference for BasisVAE,demonstrated on various toy examples as well as on single-cell gene expressiondata.

BasisVAE: Translation-invariant feature-level clustering with Variational Autoencoders