Master thesis is reaching a dead-end and supervisor doesn't seem to understand?
I'm halfway...through my masters thesis and the problem involves using a few open source software libraries to the analyse data[, which I've completed already, what should I do for the next three months?] 


You could analyse the data using different techniques, draw conclusions from your analysis, ...


  [My supervisor wants me to] explain why it performed so well, but [this is well-known].


Perhaps your supervisor wants you to demonstrate that you understand the well-known method, i.e., to explain the statistical model, the algorithm, etc.


  I am just stuck and worried on how I was going to write a thesis on this. 


You haven't mentioned the requirements for your thesis (they vary between universities). Perhaps you can edit your question to expand upon this.


  my supervisor still wants me to go deeper
  to find a link, even though there may not be one. 


Discovering the absence of a link is a research contribution (albeit, such research isn't considered so highly)


  Should I ask an [administrative] supervisor for advice? 


I don't see how an administrator can help.


  Should I just stick it out and develop a weak link between those two? 


That's one direction. Alternatively, find a better direction (and negotiated with your supervisor that you'll study that).


  Should I swap projects to something more experimental where at least
  the results are original since it was self-measured?


Your halfway, swapping projects would be risky. Perhaps you can perform experiments on your data?