They don't? One is a row in table (R^n) (order matters) and the other is a set of points (R^nxd).

If you consider the whole table, any dataSET is like point clouds.

The table is the point cloud the row is the point. The symmetry is permutations of rows or permutations of points.

In which case would you use the whole table?

Well yeah, there's no permutation symmetry between columns. (Unless there is...)

Then as parent said, almost all datasets are like point cloud, except time-series datasets.

Yeah, they are.

Oh that's interesting. Can you say more? Haven't seen much relating the two topics before.

A row in a table of data is an point in R^n. I'm not sure how much there is to write about it other than to say, that's a point cloud.

what's the intuition for why that might be desirable? I can sort of see that you might care to consider the relation between a given row and other rows (not disimilar to something like kernel methods) and then you can use something like Deep Sets[1] to featurize the data?

[1] https://arxiv.org/abs/1703.06114

I think the way it works is, you have one network that produces global permutation-invariant (maintained so by training loss) metrics and another that recognizes based on those metrics. The big prior you're putting in is that the order of the points doesn't matter. Relationships between points do matter but only in a permutation-invariant way. I would recommend reading the literature because of course, it's not my idea. :)

No, that's a point.

The table's the point cloud. I guess if you want to be really pedantic about grammar then I should point out that a set of one item is still a set. :-)

True - I misread your post. Your first post was intriguing but the second was dismissive. Surely there's more to be said than data sets are point clouds? Images are points in R^N too, right?

If your unit of recognition was a set of images, and not an image alone, then you would have permutation symmetry and want to use point cloud techniques to design your first layer. So yes images are points in R^N.

Oh thanks, this was not clear from your other posts: the whole table is used as a data point, not the line. Much clearer now, why you would compare this to point clouds

Which work do you suggest?