k -spaces: Mixtures of Gaussian latent variable models

Principal component analysis (PCA) and k -means clustering are two seemingly different methods for dimension reduction and clustering, respectively, but can be understood as special cases of inference in a Gaussian latent variable model framework. We leverage this insight to develop a probabilistic framework and methods for simultaneous dimension reduction, clustering, and latent space learning that are efficient and interpretable, and that can replace current ad hoc combinations of PCA and clustering. The algorithm, k -spaces, has broad applicability, which we demonstrate in several distinct genomic settings. In particular, we show how k -spaces can be used to model gene expression in quantitative hybridization chain reaction (qHCR) images, for inference in epigenomics, and for dimension reduction of single-cell RNA-sequencing data.