Sparse and Orthogonal Low-rank Collective Matrix Factorization (solrCMF): Efficient data integration in flexible layouts

Abstract: Interest in unsupervised methods for joint analysis of heterogeneous data sources has risen in recent years. Low-rank latent factor models have proven to be an effective tool for data integration and have been extended to a large number of data source layouts. Of particular interest is the separation of variation present in data sources into shared and individual subspaces. In addition, interpretability of estimated latent factors is crucial to further understanding. We present sparse and orthogonal low-rank Collective Matrix Factorization (solrCMF) to estimate low-rank latent factor models for flexible data layouts. These encompass traditional multi-view (one group, multiple data types) and multi-grid (multiple groups, multiple data types) layouts, as well as augmented layouts, which allow the inclusion of side information between data types or groups. In addition, solrCMF allows tensor-like layouts (repeated layers), estimates interpretable factors, and determines variation structure among factors and data sources. Using a penalized optimization approach, we automatically separate variability into the globally and partially shared as well as individual components and estimate sparse representations of factors. To further increase interpretability of factors, we enforce orthogonality between them. Estimation is performed efficiently in a recent multi-block ADMM framework which we adapted to support embedded manifold constraints. The performance of solrCMF is demonstrated in simulation studies and compares favorably to existing methods.