Editor Comments to the Author: Although most of the points raised by the reviewers have been addressed satisfactorily, the paper still needs some minor corrections and clarifications. I'd ask the authors to take into account the points raised by Rev #1 in their revision and, possibly, the one raised by Rev #3 concerning comparisons (although it's not mandatory). ******************** Reviewer Comments Reviewer: 1 Recommendation: Author Should Prepare A Minor Revision Comments: The new experiments clearly add to the contribution of this paper, and most of my concerns from my previous review have been addressed. I recommend an accept with some corrections and clarifications, which are elaborated below. The main one is to clarify yet again the presentation of the bundle method, which is important as bundle methods are not in the mainstream machine learning toolbox yet. The new presentation is extremely confusing (and actually looks incorrect). In [37] notation, they define a_(i+1) as the subgradient of Remp(w) at w_i, and b_(i+1) as Remp(w_i)-. Now in the revision, they write in algorithm 2 "compute loss b_i as described in algorithm 1, lines 6-12" which actually doesn't mention that b_i should be Remp(w_(i-1))-, so one would normally understand that b_i is simply the normalized empirical loss computed at line 12, which, unless I again misunderstood the poor presentation in [37], is incorrect. If the authors insist to say as few words as possible about BMRM as seems to be the case, they should at least implement the following clarification changes. 1) Don't mention the set W which is not used explicitly in the current presentation of alg. 1 & 2. 2) Define explicitly a_i = 1/n sum Psi_n(yhat) and b_i = 1/n sum_n Delta(yhat, y^n) - in the description of algorithm 2. Those changes would make the algorithm somewhat understandable and sufficient for knowing at least what it entails. Moreover, I forgot to mention this in my first review, but it is quite surprising that learning w doesn't increase the running time. It seems that the running time for learning should scale as the number of iterations of BRMR times the time to do inference on the training set. How many iterations were needed for BRMR? The authors should clarify this surprising element in the revision. Other points: 1) They haven't implemented my correction number 1 from my last review: in the second paragraph of IV-A, they are *not* finding a function g: G x G x W -> Y which minimizes the prediction loss; they are choosing a function g_w: G x G -> Y amongst a parametrized family. 2) A few typos should still be corrected (e.g. a missing space between words in paragraph below equation 5b and in paragraph V-B. 3) In section IV-D, for proper orientation of the reader familiar with the machine learning literature, start the first paragraph by saying that you are going to follow the *large-margin* learning approach of [33]. 4) With the code debugged, the difference between learning with linear features and quadratic features has decreased, and even inverted in some cases. The authors mention at several occasions that this could be due to the approximation used for the quadratic case. One way to get more insights into this phenomenon would be to use several different levels of quality of approximation for the quadratic assignment inference, and explore how much the final performance is impacted by it. ============= 1. Which category describes this manuscript?: Research/Technology 2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Very Relevant 1. Please evaluate the significance of the manuscript’s research contribution.: Good 2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : As before. The experimental section is more complete in this revision though, and provide more insights in the contribution of the elements of the model. 3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Yes 4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Compelling experiments; clearly state of the art 1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes 2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate 3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes 4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Could be improved 5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Readable - but requires some effort to understand 6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right Please rate the manuscript overall. Explain your choice.: Good *********************************** Reviewer: 2 Recommendation: Accept With No Changes Comments: The authors have addressed all the issues raised ============= 1. Which category describes this manuscript?: Research/Technology 2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Relevant 1. Please evaluate the significance of the manuscript’s research contribution.: Good 2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : The authors present an approach to learn the compatibility coefficient for graph matching, thus substantially improving the performance of state of the art matching algorithms. 3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Yes 4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Compelling experiments; clearly state of the art 1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes 2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate 3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes 4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Satisfactory 5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Easy to read 6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right Please rate the manuscript overall. Explain your choice.: Good ***************************** Reviewer: 3 Recommendation: Accept With No Changes Comments: The authors have addressed most of the concerns I had with the previous submission. A comparison with "Word alignment via quadratic assignment" would have been useful though, so would've been a comparison with GA with a more reasonable scaling of the quadratic vs linear term (for example scaling each of those so that they have same total contribution). ====================== 1. Which category describes this manuscript?: Research/Technology 2. How relevant is this manuscript to the readers of this periodical? If you answer Not very relevant or Irrelevant please explain your rating under Public Comments below.: Very Relevant 1. Please evaluate the significance of the manuscript’s research contribution.: Good 2. Please explain how this manuscript advances this field of research and/or contributes something new to the literature. : This manuscript presents an algorithm for supervised learning of compatibility functions for graph matching. Given a training set consisting of graph pairs and associated ground truth assignment matrices, the algorithm optimizes the empirical risk (plus some regularization term) using a linear model for the compatibility functions. The dual of the program involves a factorial number of constraints, and is solved approximately using column generation. Each iteration of learning involves (approximate) solving of graph matching problems on the training set. This paper handles learning in the general graph matching case, as opposed to previous approaches. 3. Is the manuscript technically sound? In the Public Comments section, please provide detailed explanations to support your assessment: Appears to be - but didn't check completely 4. How thorough is the experimental validation (where appropriate)? Please discuss any shortcomings in the Public Comments section.: Compelling experiments; clearly state of the art 1. Are the title, abstract, and keywords appropriate? If not, please comment in the Public Comments section.: Yes 2. Does the manuscript contain sufficient and appropriate references? Please comment and include additional suggested references in the Public Comments section.: References are sufficient and appropriate 3. Does the introduction state the objectives of the manuscript in terms that encourage the reader to read on? If not, please explain your answer in the Public Comments section.: Yes 4. How would you rate the organization of the manuscript? Is it focused? Please elaborate with suggestions for reorganization in the Public Comments section.: Satisfactory 5. Please rate the readability of the manuscript. Explain your rating under Public Comments below. : Easy to read 6. How is the length of the manuscript? If changes are suggested, please make explicit recommendations in the Public Comments section.: About right Please rate the manuscript overall. Explain your choice.: Excellent