Name of Reviewer ------------------ Ankit Gupta Key Contribution ------------------ Summarize the paper's main contribution(s). Address yourself to both the class and to the authors, both of whom should be able to agree with your summary. The key contribution of the paper is to formulate nearest subspace search problem for linear and affine subsapces in dimension 'd' as nearest neighbour search problem in 'd^2'. Refinements like random projections have been introduced to increase the efficiency of the algorithm. The results shown are encouraging. Novelty -------- Does this paper describe novel work? If you deem the paper to lack novelty please cite explicitly the published prior work which supports your claim. Citations should be sufficient to locate the paper and page unambiguously. Do not cite entire textbooks without a page reference. Yes, this paper does present novel work. Though the idea of formulating the problem as nearest neighbour search existed earlier (by Magen as cited in the paper) but the mapping space in this paper has much lower dimensions than earlier work (polynomial than exponential). Reference to prior work ----------------------- Please cite explicitly any prior work which the paper should cite. All relevant papers to my knowledge have been cited. Clarity ------- Does it set out the motivation for the work, relationship to previous work, details of the theory and methods, experimental results and conclusions as well as can be expected in the limited space available? Can the paper be read and understood by a competent graduate student? Are terms defined before they are used? Is appropriate citation made for techniques used? The paper does set out the motivation and relationship to earlier work. I feel understanding the full derivations in the paper requires a strong knowledge of linear algebra. The derivation for linear subspaces is comprehensive and they build the argument for affine spaces on the similar lines, but to me, they do a bad job here. Appropriate citations have been made for the techniques used (mainly the ANN approaches). Technical Correctness --------------------- You should be able to follow each derivation in most papers. If there are certain steps which make overly large leaps, be specific here about which ones you had to skip. As said, the paper involves a strong background of linear algebra. Some steps involve results on relationships between null spaces, column spaces etc which have not been explained and I found them a bit difficult to follow. Given that, one can follow the derivations. Experimental Validation ----------------------- For experimental papers, how convinced are you that the main parameters of the algorithms under test have been exercised? Does the test set exercise the failure modes of the algorithm? For theoretical papers, have worked examples been used to sanity-check theorems? Speak about both positive and negative aspects of the paper's evaluation. The paper evaluates the performance for the use of subspaces in image reconstruction, face and patch recognition. It does not very well test out the effect of random projections into reduced dimensions on the system performance. Though the time taken will be lesser, it might be interesting to see if the numerical advantage leads to any disadvantage in the high level solution. Overall Evaluation ------------------ The paper clearly presents a novel way to model the nearest space search problem to nearest neighbour search. The mathematical modeling is rigorous and correct. Assuming subspace search has been proved to be much better for image techniques, this will have an impact over the system performance. Questions and Issues for Discussion ----------------------------------- What questions and issues are raised by this paper? What issues do you think this paper does not address well? How can the work in this paper be extended? 1. Can the nearest subspace problem be mapped to a paradigm which is linear in the number of original dimensions? 2. Are spaces other than linear and affine spaces useful and how can this method be extended for them? 3. Given we have this nice way of doing subspace search, what image and video editing algorithms can be improved or developed using this?