Predicting positive/negative experience with very few labels and labels from only one class I have video viewing data (length of session, nb of videos, etc), as well as if the user clicked on the like button. We can use the like button as a confirmation that the user had a positive viewing experience, however, only 0.1% of users click on this button. 
I would like to find a way to find users that have a similar data to those who liked the video without having them explicitly click the like button.

I thought about having the like variable be the response variable in a binary classification problem, however, not liking the video does not mean negative experience.

I also thought of maybe treating it as an unsupervised task, where I look if the liked sessions fall naturally inside a specific cluster.

Edit:  I did not make it clear, but the service is similar to Youtube, where we are trying to figure out if a user had a positive viewing experience after clicking on a video. Right now, there is no recommendation engine and this is the first part in building one.

Edit: After the answers, I am leaning more towards approaching this task as an unsupervised learning task, rather than supervised.

Any thoughts how to approach this problem?
Thanks
This is not a data science solution, but wouldn't the fact that the user watched the video in the first place (took the time to find and locate the video then started the video) imply that the user have some interest in that particular video over users that never interacted with the video? I would consider the fact that the entry exists as a positive response, the lack of a "like" as a neutral response, and (maybe?) the lack of watching it as a negative response. It, of course, depends heavily on the source and assumptions of your dataset.

Nonetheless, I agree that clustering the videos with likes is a good starting point in this situation, and that would definitely be my first gut instinct thing to do.