Simplex2vec Backward: From Vectors Back to Simplicial Complex
Simplicial neural networks (SNNs) were proposed to generate higher-order simplicial complex representations as vectors that encode not only pairwise relationships but also higher-order interactions between nodes. Although these vectors allowing us to consider richer data representations compared to typical graph convolution, most real-world graphs associated with molecule or human-related activities are often sensitive and might contain confidential information, e.g., molecular geometry or friend lists. However, little works investigate the potential threats for these simplicial complexes (higher-order interactions between nodes). We name this threat by Simplicial Complexes Reconstruction Attack (SCRA) and conduct this attack by studying whether the vectors can be inverted to (approximately) recover the simplicial complexes who used to generate them. Specifically, we first generate the vectors via a k-simplex2vec approach that extends the node2vec algorithm to simplices of higher dimensions to associate Euclidean vectors to simplicial complexes. We then present a Simplex2vec Backward algorithm to perform the SCRA on k-simplex2vec vectors by pointwise mutual information (PMI) matrix reconstruction.