Algorithm 1:

Assigning mutational signatures to samples with SigProfilerAssignment

	Input: $\overrightarrow{\mathit{v}}\in {\mathbb{N}}_{+}^{\xi \times 1}$ (a vector corresponding to a set of mutations in a sample) and $\mathit{S}\in {\mathbb{R}}_{+}^{\xi \times 1}$ (a matrix corresponding to a set of $n$ known mutational signatures)
	Output: $\overrightarrow{\mathit{a}}\in {\mathbb{N}}_{+}^{n\times 1}$ (the vector reflecting the activities of the $n$ known signatures in sample $\overrightarrow{\mathit{v}}$)
1:	${ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, $\overrightarrow{a}=\text{calcNNLS}(\overrightarrow{v},\mathit{S})$
	${\mathit{S}}^{\text{all}}=\mathit{S}$
2:	While FLAG = True:
3:	${ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, $\mathit{S}=\mathit{r}\mathit{emoveSignatures}(\overrightarrow{v},\mathit{S},{ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}})$
4:	${ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, $\mathit{S}=\mathit{addSignatures}(\overrightarrow{\mathit{v}},{\mathit{S}}^{\text{all}},\mathit{S},{ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}})$
5:	Set FLAG = False if $\mathit{S}$ remains constant and there is no addition or removal of signatures
	END While
6:	${ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}}$, $\overrightarrow{\mathit{a}}=\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{N}\mathit{N}\mathit{L}\mathit{S}(\overrightarrow{v},\mathit{S})$
7:	Return $\overrightarrow{\mathit{a}}$
8:	FUNCTION removeSignatures $(\overrightarrow{\mathit{v}},\mathit{S},{ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}})$
9:	While FLAG = True:
10:	For $\mathit{j}$ in 1 to size($\mathit{S}$, 2) do	// loop from 1 to the total number of signatures in $\mathit{S}$
11:	$\stackrel{\mathit{ˆ}}{\mathit{S}}=\mathit{S}[:,-\mathit{j}]$	// remove the jth signature from $\mathit{S}$
12:	$\in \left[j\right]$, ${\overrightarrow{\mathit{a}}}_{\mathit{j}}=\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{N}\mathit{N}\mathit{L}\mathit{S}(\overrightarrow{\mathit{v}},\widehat{\mathit{S}})$
	END For
13:	minIndex, $\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\mathrm{m}\mathrm{i}\mathrm{n}(ϵ)$	// find the signature set with least relative error
14:	If $(\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}-{ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}}\le 0.01)$
15:	$\mathit{S}=\mathit{S}[:,-\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}]$
	else
16:	Return minValue, $\mathit{S}$
	END If
	END While
	END removeSignatures
17:	FUNCTION addSignatures $(\overrightarrow{\mathit{v}},{\mathit{S}}^{\text{all}},\mathit{S},{ϵ}_{\mathrm{m}\mathrm{i}\mathrm{n}})$
18:	While FLAG = True:
19:	For $\mathit{p}$ in 1 to size(${\mathit{S}}^{\text{all}}$, 2) do	// loop from 1 to the total number of signatures in ${\mathit{S}}^{\text{all}}$
20:	$\widehat{\mathit{S}}=\left[\mathit{S};{\mathit{S}}^{\text{all}}[:,\mathit{p}]\right]$	// add the pth signature from ${\mathit{S}}^{\text{all}}$
21:	$ϵ\left[j\right]$, ${\overrightarrow{\mathit{a}}}_{\mathit{j}}=\mathit{c}\mathit{a}\mathit{l}\mathit{c}\mathit{N}\mathit{N}\mathit{L}\mathit{S}(\overrightarrow{\mathit{v}},\widehat{\mathit{S}})$
	END For
22:	minIndex, $\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}=\mathrm{m}\mathrm{i}\mathrm{n}(ϵ)$	// find the signature set with least relative error
23:	If $\left({ϵ}_{min}-\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\ge 0.05\right)$
24:	$\mathit{S}=\left[\mathit{S};{\mathit{S}}^{\text{all}}[:,\text{minValue}]\right]$
	else
25:	Return minValue, $\mathit{S}$
	END If
	END While
	END addSignatures
26:	FUNCTION calcNNLS $(\overrightarrow{\mathit{v}},\mathit{S})$
27:	$\overrightarrow{\mathit{a}}=nnls(\mathit{S},\overrightarrow{\mathit{v}})$	// Calculating NNLS with the Lawson-Hanson method
28:	$ϵ=\parallel \overrightarrow{\mathit{v}}-\mathit{S}\overrightarrow{\mathit{a}}{\parallel }_2^2/\parallel \overrightarrow{\mathit{v}}{\parallel }_2^2$	// Computing relative error
29:	Return $ϵ$, $\overrightarrow{\mathit{a}}$
	END calcNNLS