Single-cell data integration across weakly linked modalities
Fig 1
(a) The input modality matrices and
share
linked features. Weighted adjacency cell graphs
and
are constructed through the akNN module. (b) Linked features are embedded via the hypergraph operator
to generate initial embeddings, followed by a Many-to-Many (M-to-M) matching process to obtain the initial matching
. (c) The workflow iteratively updates cell embeddings and matching for
iterations. Each loop involves
, Canonical Correlation Analysis (CCA) [27], and M-to-M matching. The final outputs are the optimized joint embeddings
and the 1-to-N matching
. (d) Feature similarity
is calculated to transition from a constant k in standard kNN to a cell-specific adaptive
, yielding the final graph
. (e) For a target cell i, local and global message-passing branches generate embeddings
and
, respectively. Contrastive learning is employed between the two branches to enhance representation robustness, followed by a fusion step to obtain the final learned embedding
.