Test statistic 9: Do genes a and b interact when a is expressed by cell i (that belongs to cell type t) and b by spatially nearby cells (that belong to cell type u)?

In addition to visualizing the cell-type-agnostic gene pair scores (defined in Test statistic 7), the equation below represents the individual cell/spot values when cell-type identity is considered:

\[ H_{i \in C_t}^{t,u} (ab) = \sum_{j \in C_u}^{} w_{ij}X_{ai}X_{bj} \]

This equation is only used for visualization purposes, and no statistical test has been implemented.