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Abstract Single cell data integration methods aim to integrate cells across data batches and modalities, and data integration tasks can be categorized into horizontal, vertical, diagonal, and mosaic integration, where mosaic integration is the most general and challenging case with few methods developed. We propose scMoMaT, a method that is able to integrate single cell multi-omics data under the mosaic integration scenario using matrix tri-factorization. During integration, scMoMaT is also able to uncover the cluster specific bio-markers across modalities. These multi-modal bio-markers are used to interpret and annotate the clusters to cell types. Moreover, scMoMaT can integrate cell batches with unequal cell type compositions. Applying scMoMaT to multiple real and simulated datasets demonstrated these features of scMoMaT and showed that scMoMaT has superior performance compared to existing methods. Specifically, we show that integrated cell embedding combined with learned bio-markers lead to cell type annotations of higher quality or resolution compared to their original annotations. 

Abstract Motivation The study of the evolutionary history of biological networks enables deep functional understanding of various bio-molecular processes. Network growth models, such as the Duplication–Mutation with Complementarity (DMC) model, provide a principled approach to characterizing the evolution of protein–protein interactions (PPIs) based on duplication and divergence. Current methods for model-based ancestral network reconstruction primarily use greedy heuristics and yield sub-optimal solutions. Results We present a new Integer Linear Programming (ILP) solution for maximum likelihood reconstruction of ancestral PPI networks using the DMC model. We prove the correctness of our solution that is designed to find the optimal solution. It can also use efficient heuristics from general-purpose ILP solvers to obtain multiple optimal and near-optimal solutions that may be useful in many applications. Experiments on synthetic data show that our ILP obtains solutions with higher likelihood than those from previous methods, and is robust to noise and model mismatch. We evaluate our algorithm on two real PPI networks, with proteins from the families of bZIP transcription factors and the Commander complex. On both the networks, solutions from our ILP have higher likelihood and are in better agreement with independent biological evidence from other studies. Availability and implementation A Python implementation is available at https://bitbucket.org/cdal/network-reconstruction. Supplementary information Supplementary data are available at Bioinformatics online.