problem about the graph symmetry

[InvincibleWza1999]

Thank you for your excellent work! But I have a problem about the graph symmetry. The article says the dependency patterns between sensors need not be symmetric. However, in the case without prior information, the candidate relation graph is fully-connected, and the similarity matrix is symmetric, while the topk operation does not change its symmetry. Does it mean the learned adjacency matrix A is symmetric? Thank you for your answering!

[d-ailin]

Hi, thanks for your interest!

While the similarity matrix is symmetric, applying the top-k operation directly on this matrix does not necessarily result in a symmetric adjacency matrix, as the top-k operation is selecting top-k elements in each row independently, you might include $S_{ij}$ in row i but not $S_{ji}$ in row j as the top-k neighbors in row i and j could be different ($S$ is a symmetric matrix).