---------- The main section of the paper (section 3) seems carelessly written. Some obvious weaknesses: - Algorithm 1 seems more confusing, than clarifying: a) Shouldn't the gradient step be taken in the direction of the gradient of the loss with respect to Theta? b) There is no description of the variables, most importantly X and f. It is better for the reader to define them in the algorithm than later in the text. Otherwise, the algorithm definition seems unnecessary. - Equation (1) is very unclear: a) Is the purpose to define a loss function or the optimization problem? It seems that it is mixing both. b) The optimization variable x is defined to be in R^n. Probably it is meant to be in R^k? c) The constraints notation (s.t. C(A, x)) is rather unusual. - It is briefly mentioned that an alternating direction method is used to solve the min-min problem. Which method? - The constraints in equation (2) are identical to the ones in equation (3). They can be mentioned as such to gain space. - In section 4.1, line 194, K = 10, presumably refers to the number of atoms in the dictionary, namely it should be a small k? The same holds for section 4.4, line 285. - In section 4.1, why is the regularizer coefficient gamma set to zero? Intuitively, structured sparcity should be particularly helpful in finding keypoint correspondences. What is the effect on the solution when gamma is larger than zero? The experimental section of the paper seems well written (with a few exceptions, see above). Nevertheless, the experiments in 4.2 and 4.3 each compare to only one existing work. In general, I can see the idea of the paper has merit, but the carelessness in the formulations in the main part and the lack of comparisons to other works make me hesitant to accept it as is at NIPS.
- It is briefly mentioned that an alternating direction method is used to solve the min-min problem. Which method?