In machine learning how to find feature interdepencies?
For me it seems you are looking for Association Rule Learning. A quite simple example for an algorithm you could use is the Apriori Algorithm. You could try that one first and see if it does what you want to achieve. Then you can take a look into more sophisticated algorithms. 

Generally these algorithms try to find associations between your features. E.g. they are able to find the implication, that many people who buy Coca Cola &amp; Beer, will buy a pack of chips - if supported by the data: 

$(Coca Cola, Beer)\implies(Chips)$.