In this article, I will demonstrate how one can perform graph based across modalities integration of single cell Omics (scOmics) data by using graph intersection approach with Igraph and UMAP.

This is the **twentieth** article from the column **Mathematical Statistics and Machine Learning for Life Sciences** where I try to explain some mysterious analytical techniques used in Bioinformatics and Computational Biology in a simple way. Data integration is an important next step for improving analysis accuracy by utilizing synergistic effects via combining multiple sources of information. In Computational Biology and Biomedicine, data integration is making particular advances in Single Cell research area. Last year, **Nature** recognized **Single Cell Multimodal Omics Integration** as a **method of the year 2019**. In this article, I will demonstrate how one can perform graph based across modalities integration of single cell Omics (**scOmics**) data by using **graph intersection** approach with **Igraph** and** UMAP**.

When combining data originating from different statistical distributions, it is probably not a good idea to simply concatenate them together without taking into account their individual distributions as some of them might be of binary, categorical or continuous nature. Working with scOmics data one often deals with continuous scRNAseq (transcriptomics) / scProteomics (proteomics) and binary scBSseq (methylation) / scATAseq (open chromatin region) data. Suppose the individual data types are capable of distinguishing cells from sick and healthy individuals with an accuracy of 78%, 83% and 75% (the numbers are made up). Then, one expectation from combining the multiple scOmics together would be a **boost in prediction accuracy** (e.g. up to 96%) due to reduction of technology-specific noise and enhancing the consistent across scOmics signal.

There can be different approaches to combining the individual scOmics. One possible way could be converting the scOmics into a common non-parametric space where they loose the memory about their technology of origin. This is how e.g. Artificial Neural Networks (ANN) are capable of collapsing multiple sources of information, that I describes in details in one of my previous posts. The **Similarity Network Fusion (SNF)** also belongs to this type of approach. Another approach would be explicitly model the individual data distributions and combining them as a **joint probability** using Bayes rule. Finally, one can try to extract common variation (i.e. disentangle the technology-specific and shared variation in the data) and factor it (split into orthogonal components) for better interpretation, a way used by PLS, CCA and Factor Analysis.

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