Algorithm 1.

Multiple adjacency spectral embedding (MASE)

Input: Sample of graphs A⁽¹⁾,…, A^(m); embedding dimensions d and

{d_{i}}_{i = 1}^{m}

1. For each i ∈ [m], obtain the adjacency spectral embedding of A⁽ⁱ⁾ on d_i dimensions, and denote it by

{\hat{V}}^{(i)} \in R^{n \times d_{i}}

2. Let

\hat{U} = ({\hat{V}}^{(1)} \dots {\hat{V}}^{(m)})

be the

n \times (\sum_{i = 1}^{m} d_{i})

matrix of concatenated spectral embeddings.

3. Define

\hat{V} \in R^{n \times d}

as the matrix containing the d leading left singular values of

\hat{U}

4. For each i ∈ [m], set

{\hat{R}}^{(i)} = {\hat{V}}^{⊤} A^{(i)} \hat{V}

Output:

\hat{V}, {{\hat{R}}^{(i)}}_{i = 1}^{m}