I was going through various evaluation metrics that can be used to evaluate recommendation metrics. Mainly my focus was on ranking metrics which considers the order of recommendation as well. I found MAP at k to be one of the solution as it considers the order as well. But it penalizes the wrong ordered recommendations completely, i.e. suppose the correct recommendations order is [A,B,C] and we have recommended [A,C,B] . So, it will penalize both C and B completely. But what i want is that instead of completely penalizing these recommendations, it should give some values to them.
I heard about rank correlation metric that can be used for such cases but i am not clear about that. Any help on this will be appreciated.