apply this to d-dim(d>1) regression task

[swc1204]

thank you for your greate job!
if i would like to apply this to d-dim(d>1) regression task(target has d-min), how should change the ranksim.py ?

[yugongg]

Hi, thanks for your interest!

To extend the method to d-dim (d>1) labels, Eq.2 in the paper needs to be modified. The core idea is how to produce a similarity matrix -- we need to measure the label similarity that can be used for ranking (which is used as supervision).
If it's 1-dim, it's straightforward (e.g. 70 > 25 > 21 > 1, and we used negative absolute distance);
If it's d-dim (d>1), you can use the same way as how we defined sigma_z (refer to Eq.3, and also ''Different choices for feature similarity function sigma_z'' in section 4.4). But this strategy has an implicit assumption that every dimension is homogeneous. For some heterogeneous multi-dimensional label, you may need to define some other similarity functions.

[swc1204]

thank you for your reply！
i think the cosine similarity function is suitable for my task,so i change the code as following, is there anything i should pay attention,like the RrueRanker ?

# Compute gaze similarities
yyt = torch.matmul(F.normalize(y.view(y.size(0), -1)), F.normalize(y.view(y.size(0), -1)).permute(1, 0))

# Compute features similarities
xxt = torch.matmul(F.normalize(x.view(x.size(0),-1)), F.normalize(x.view(x.size(0),-1)).permute(1,0))

# Compute ranking loss
for i in range(len(y)):
    label_ranks = TrueRanker.apply(yyt[i].unsqueeze(dim=0), lambda_val)
    feature_ranks = TrueRanker.apply(xxt[i].unsqueeze(dim=0), lambda_val)
    loss += F.mse_loss(feature_ranks, label_ranks)

[yugongg]

TrueRanker is not needed for label_ranks, because label_ranks is ground-truth and TrueRanker is used to make the ranking on the features to be differentiable. You can directly transform the similarity matrix to the ranking of matrix, by using rank_normalised function on each row of yyt.

[swc1204]

i got it,thank you for your patient solution