Recently, in my research lab we were able to achieve a performance of X % for some problem. This X is far better than the performance Y which was achieved by some other research group for the exact problem, very recently (two months ago).
Yes, we can always compare X and Y and publish the paper alone. But, I was thinking that it is better to collaborate with that research group and share with them the results of our approach.
Should my research group collaborate with them?
Is this a proper way of collaboration?
Should they feel that our group is weaker than they are and that this is why we are trying to collaborate (a feeling of insecurity)?
Could I get some suggestions on this?