Algorithm 1.

The iterative estimation procedure of sample indicator vector and gene score vector in mCGfinder.

Algorithm 1 mCGfinder: iterative estimation procedure

Input: mutation matrix ${\mathit{X}}_{n\times p}$; graph Laplacian matrix L;

Output: sample indicator vector s 1; gene score vector g 1.

1: set λ L ← 0.1

2: ${\mathit{s}}_1^{\mathrm{(0)}}\leftarrow {\mathbf{1}}_n$ and ${\mathit{g}}_1^{\mathrm{(0)}}\leftarrow {\left(n{\mathit{I}}_p+{\lambda }_L\mathit{L}\right)}^{-1}\left({\mathit{X}}^{\mathrm{T}}{\mathbf{1}}_n\right)$

3: repeat

4: ${\mathit{g}}_1^{(k+\mathrm{1)}}\leftarrow {\left({\Vert {\mathit{s}}_1^{(k)}\Vert }_2^2{\mathit{I}}_p+{\lambda }_L\mathit{L}\right)}^{-1}\left({\mathit{X}}^{\mathrm{T}}{\mathit{s}}_1^{(k)}\right)$

6: ${\mathit{s}}_1^{(k+\mathrm{1)}}\leftarrow {\mathit{I}}_{\left[\mathrm{0,}\infty \right)}\left(2\mathit{X}{\mathit{g}}_1^{(k+\mathrm{1)}}-{\Vert {\mathit{g}}_1^{(k+\mathrm{1)}}\Vert }_2^2\right)$

6: k ← k + 1

7: until Convergence

8: return ${\mathit{s}}_1\leftarrow {\mathit{s}}_1^{(\infty )}$ and ${\mathit{g}}_1\leftarrow {\mathit{g}}_1^{(\infty )}$

Note:  1 n is an n × 1 vector with all coefficients being 1; Indicator function I A(x) returns a logical vector if x i ∈ A.