Image clustering with deep learning I want to cluster image, since varibility intra and inter class of images is huge I think reducing dimensions with a convolutional autoencodeur can be a good tools. Then I apply clustering on the feature vector 

My question: is there a theorical link between my convolutional autoencodeur loss and the potential for clustering of my extracted feature vector? 

To add more detail, can we says if I can minimise loss then it'll be easier to do clustering on feature vector? My intuition tel me answer is NO

But if we can't use loss to select potential best model for clustering, then isn't it almost impossible to do a good clustering using this methodology?
Few clustering algorithms have any kind of loss. That is pretty much only k-means and a few closely related methods that fit this narrow world view of "everything is optimizing a loss".

Now if your features would minimize the same loss, then the result should be close to just doing k-means on the raw pixels - which is known to not work well. You do want features that lose a lot of irrelevant information.