2. The method as recited in claim 1 further comprising: maximizing an average of pair-wise labeled information of a query such that 1  d i > d j : q k  ⁢ ∑ d i > d j : qk ⁢ tr ⁢ { W T ⁡ ( ( 2 ⁢ q k - d i - d j ) ⁢ ( d i - d j ) T ) ⁢ W } ⁢ ξ kij represents the pair-wise ranked data for the query represented as q k , wherein: |d i <d j :q k | represents the number of the pair-wise labeled data, and ξ kij represents a weight characterizing importance of a ranked pair for a given query.
2. The method as recited in claim 1 further comprising: maximizing an average of pair-wise labeled information of a query such that 1  d i > d j : q k  ⁢ ∑ d i > d j : qk ⁢ tr ⁢ { W T ⁡ ( ( 2 ⁢ q k - d i - d j ) ⁢ ( d i - d j ) T ) ⁢ W } ⁢ ξ kij represents the pair-wise ranked data for the query represented as q k , wherein: |d i <d j :q k | represents the number of the pair-wise labeled data, and ξ kij represents a weight characterizing importance of a ranked pair for a given query. 3. The method as recited in claim 2 wherein optimizing 1  d i > d j : q k  ⁢ ∑ d i > d j : qk ⁢ tr ⁢ { W T ⁡ ( ( 2 ⁢ q k - d i - d j ) ⁢ ( d i - d j ) T ) ⁢ W } ⁢ ξ kij embodies a closed form solution.