Negative sampling on block diagonal matrix

[kristianeschenburg]

Hi

I’m interested in doing negative sampling on a graph for node classification. My training graph is a block diagonal matrix where each block is a single training example. I want to perform negative sampling on each block independently – that is, I want to generate negative samples for each block using only the nodes from that same block.

Apart from not calling dgl.batch(list_of_graphs) and iterating over the individual graphs, how can I go about doing this?

Thanks

k

[BarclayII]

As far as I understand, negative sampling is more common in link prediction tasks. However, it seems that you are doing node classification. Could you elaborate on what the negative examples are?

[kristianeschenburg]

In this case, I’m working on a segmentation task, where the nodes are part of a triangulated mesh G=(V,E). I’m interested in implementing a similar loss function to that described by GraphSAGE

J_{G}(z_{u}) = -log(\sigma(z_{u}^{T}z_{v})) - Q \cdot \mathbb{E}_{v_{n}\sim P_{n}(v)}log(\sigma(z_{u}^{T}z_{v_{n}}))

so the negative samples will essentially just generate random links between nodes in the mesh. However, I have many meshes in my training data, each with their own node feature matrices. I do not want to shuffle node features across meshes when computing this loss.

k

[BarclayII]

Is your negative example a random graph with the same number of nodes? If so, you will need to generate the negative example graph individually, and batch() them altogether.

Other than that, something like “generate a random integer array with each element having its own low and high range” can help you:

def rand_int(lows, highs):
    diff = highs - lows
    rand = (torch.rand(len(lows)) * diff).long()
    return lows + rand

[kristianeschenburg]

Hi @BarclayII

Thank you – yes, this is what I ended up doing. It seems to be a reasonable approach thus far.

k