Table 2.

Notations

Notation	Definition
n, m	# of samples and features (e.g., genes), respectively.
X ∈ ${\mathbb{R}}^{m\times n}$	genomic profile matrix.
β ∈ ${\mathbb{R}}^{m\times 1}$	coefficients of features to be learned by the model.
$y\in {\mathbb{R}}^{n\times 1}$	responses for regression or labels for classification, y = (y 1, …, y n)T.
$W\in {\mathbb{R}}^{m\times m}$	symmetric adjacency matrix of an undirected molecular network.
D x	diagonal matrix with vector x on the diagonal.
$S\in {\mathbb{R}}^{m\times m}$	normalized symmetric adjacency matrix: $S=D_w^{-\frac{1}{2}}{WD}_w^{-\frac{1}{2}}$, where w is the row sum of W.
$L\in {\mathbb{R}}^{m\times m}$	normalized graph Laplacian: L = I − S.
β T Lβ	graph Laplacian regularization: ${\beta }^{\mathrm{T}}L=\frac{1}{2}{\sum }_{i,j}{S}_{i,j}{\left({\beta }_i-{\beta }_j\right)}^2$.
$f^{\left(\mathbf{0}\right)}\in {\mathbb{R}}^{n\times 1}$	initialization for semi-supervised learning: $f^{\left(\mathbf{0}\right)}={\left\{f_1^{\left(0\right)},\dots ,f_i^{\left(0\right)},\dots ,f_n^{\left(0\right)}\right\}}^{\mathrm{T}}$, where $f_i^{\left(\mathbf{0}\right)}\in \left\{-1,0,+1\right\}$. 0 is assigned if there are additional unlabeled data for semi-supervised learning.
$f\in {\mathbb{R}}^{n\times 1}$	Predictions by semi-supervised learning: $f={\left\{f_1,\dots ,f_n\right\}}^{\mathrm{T}}$.
λ, λ 1, λ 2	positive hyper-parameters to weight the cost terms.