Table 1 Algorithm for iterative multi-omics imputation

A: Initialize with replacing all missing values in all matrices G _i , i = 1, 2, 3 by self-imputation methods to obtain complete matrices {G ⁽⁰⁾ _i }.

B: for each iteration h, 

 (1).

  a. Self-impute G ₁ based on G ^{(h − 1)}₁ ; Cross-impute G ₁ by G ^{(h − 1)}₂ , G ^h − 1₃ using multi-omics imputation method to obtain G ^(h)₁ .

  b. Self-impute G ₂ based on G ^{(h − 1)}₂ ; Cross-impute G ₂ by G ^(h)₁ , using multi-omics imputation method to obtain G ^(h)₂ .

  c. Self-impute G ₃ based on G ^{(h − 1)}₃ ; Cross-impute G ₃ by G ^(h)₁ , G ^(h)₂ using multi-omics imputation method to obtain G ^(h)₃ .

 (2). Determine the sum of square of difference on the missing locations j between {G ^{(h − 1)} _i } and {G ^(h) _i }:

   \( {\delta}^h={\displaystyle \sum_j{\displaystyle \sum_i{\left({G}_i^{j,\left(h-1\right)}-{G}_i^{j,(h)}\right)}^2}} \)

C. If δ ^h ≤ τ, the iteration is stopped and output {G ^(h) _i }; otherwise go to Step 2 to continue the iteration until the convergence criteria τ is reached.