Error about transform about fugw

[TuDou-PK]

OK, Thanks for your explanation 👍

[pbarbarant]

Thanks @TuDou-PK for your interest in our repo!

FUGW basically consists in solving a Gromov-Wasserstein problem between graphs, leading to weighted assignments between source and target nodes. The problem thus differs from a domain adaptation setting as there is no geometric displacement of the points.

The idea of mapping.transform is to transport a fresh set of features from the source to the target space using a previously fitted transport plan.

Going back to your example, if you have $50$ new features (for example fMRIs contrast maps) that you want to send from a graph with $3000$ nodes to a graph supported over $9000$ nodes, you effectively want your transformed data to take the shape $[9000, 50]$.

The notion of ambient dimensions in which each graph is embedded is only relevant for the computation of the geometric cost and is not related to the number of features. @alexisthual It might be worth to emphasize this in the documentation.

I hope my explanation is clear :)

[bthirion]

@pbarbarant @alexisthual can you take a look ?

[TuDou-PK]

@pbarbarant Thanks for your reply, please help me to confirm if I understand correctly:

In your graph application, your aim is to map the 3000-node graph to the 9000-node graph, then you can do further process to compare with the mapped 9000-node graph and the target 9000-node graph. As for the node features, no matter if it's 50-dim or 100-dim, you don't care, right? Your aim only cares about the node(graph) geometry information.

Ah! Maybe I got you, that's why in your code, the array shape is like [position, node_number], then actually you treat the "node_number" as the feature, that looks make sense.

So the conclusion is POT and FUGW all are not wrong, just the aim is different?

[pbarbarant]

I believe the easiest example is an image where the underlying graph is the 2D grid and over each pixel (node of the graph) you will have a set of features which corresponds to the three RGB channels for example.

In POT's DA example, you would only work in the RGB space, thus your RGB points would move geometrically in this color space, therefore you would get a mapping between colors.

With FUGW, you also take into account the graph geometry between pixels, thus a slice of your data array at pixel $i$ would look like $[\textbf{red}_i, \textbf{green}_i, \textbf{blue}_i]$ and the total array has a size [number_of_pixel, 3], therefore you get a mapping between pixels.