3148
Global optimality is achieved since all valid regions are simultaneously taken into account , and noise can be effectively reduced by enforcing the subspace constraint .
 used for: subspace constraint, noise
Given options, please tell me the relationships of all the listed entity pairs.Output format is "relation1: word1, word2; relation2: word3, word4". 
Option: conjunction, feature of, hyponym of, used for, part of, compare, evaluate for 
Text: {0} 
 Entity Pairs:  subspace constraint, noise 
Answer:
 used for: subspace constraint, noise