UFGOT: Unbalanced Filter Graph Alignment with Optimal Transport for Cancer Subtyping Based on Multi-omics Data

The development of sequencing technologies allows us to obtain diverse omics data. However, except for a few multi-omics profiling techniques simultaneous sequencing multiple types of molecules within a sample, under more circumstances the integration of multi-omics measurements is required for joint analysis. Due to the lack of correspondence between samples or omics features, it is challenging to align data from different domains to a common domain using computational methods. With the introduction of optimal transport (OT) theory to the field of data integration, several OT-based data alignment methods have been proposed. Graph optimal transport (GOT) is a graph alignment algorithm based on Laplacian matrix and filter graph alignment with optimal transport (fGOT) introduces filters to GOT, proposing filter graph distance. However, due to the strict control of marginal distribution inherent in OT problems, their performance may be lower than expected in real-world data. Therefore, we propose unbalanced filter graph alignment with optimal transport (UFGOT), relaxing the OT marginal constraints, to find a mapping between features of different omics. We apply UFGOT for cancer subtyping using multi-omics data and compare it with general-purpose and multi-omics data-specific integration methods. UFGOT, with the introduction of an unbalanced term, outperforms fGOT and other algorithms in the performance of data integration. Additionally, we demonstrate the effectiveness of UFGOT in facilitating downstream clustering analysis. We showcase the application of UFGOT in cancer subtyping, while it is adaptable to other multi-omics data integration problems. The source codes and the analyzed datasets are available at: https://github.com/JGuan-lab/UFGOT .