Disjoint MNIST Dataset?

[kmader]

So my intuitive guess for how the MNIST dataset worked would be classifying the graph of just the positive pixels into 0-9. The example being a 2.

Is that an interesting problem to use as a benchmark for classification or is the fixed adjacency matrix and varying features better suited?

[danielegrattarola]

I've never seen what you suggest in the literature.
The 8-NN graph setting is taken from Defferrad et al. (2016), and it's interesting because it's a problem of graph signal classification: same topology, different features.

A GNN should not be able to distinguish the graph in the picture from a 5. If you remove the black pixels it should become almost impossible to classify MNIST, unless you encode spatial positions explicitly.

[kmader]

Thanks for the link, I am very news to graph NN and am just trying to get some feeling for it. The indistinguishability of 2 and 5 point makes sense but they don't get confused very often (they aren't however very accurately predicted)

The model seems to learn to recognize tips and twists very well, but struggle to count them which might be a weakness of the global attention layer. The figure shows the activation at each node for each channel.

• Without spatial information (34%)
  https://www.kaggle.com/kmader/disjoint-mnist-graph-deep-learning/

• With spatial coordinates as features of vectors (87%)
  https://www.kaggle.com/kmader/disjoint-mnist-graph-with-xy

• Dataset
  https://www.kaggle.com/kmader/mnist-based-graphs

[danielegrattarola]

Yeah, that 34% accuracy without coordinates does not surprise me. From a topology perspective, the GNN should be able to distinguish three classes depending on how many "holes" are in the graph: {1, 2, 3, 5, 7}, {4, 6, 9, 0}, {8}. I am not too sure about this claim though, I would need to think about it.

With spatial coordinates instead, it becomes a point cloud so it makes more sense. 87% seems a bit low, considering that on the original grid setting even very simple GNNs get to 99% easily, but it may be due to a number of factors.

Nice work! I am not sure that I would include it as a benchmark dataset in Spektral in order to avoid confusion, but you're doing a nice job for sure.