Paper:
Projective dictionary pair learning for pattern classification
Discriminative dictionary learning (DL) has been widely studied in various pattern classification problems. Most of the existing DL methods aim to learn a synthesis dictionary to represent the input signal while enforcing the representation coefficients and/or representation residual to be discriminative. However, the 0 or 1 -norm sparsity constraint on the representation coefficients adopted in most DL methods makes the training and testing phases time consuming. We propose a new discriminative DL framework, namely projective dictionary pair learning (DPL), which learns a synthesis dictionary and an analysis dictionary jointly to achieve the goal of signal representation and discrimination. Compared with conventional DL methods, the proposed DPL method can not only greatly reduce the time complexity in the training and testing phases, but also lead to very competitive accuracies in a variety of visual classification tasks.

Review:
This paper proposes a discriminative dictionary learning framework for both synthesis and analysis dictionaries, namely projective dictionary pair learning (DPL), where the analysis dictionary is learned by linear projection. The purpose of the method is to improve the computational efficiency of the coding process by discarding the explicit optimization of sparsity regularizers, e.g. l1/l0 norm without sacrificing the classification accuracy. While the paper is easy to follow there are several typos/grammatical errors/incorrect equation references, e.g. on page 4, (8) in the last sentence should be (9), that needs to be corrected. The paper deals with an topic that is of significant interest. Nevertheless, the proposed method has marginal novelty because there are related methods already existing in the literature. For instance, see the following missing but very related reference:Zhizhao Feng*, Meng Yang*, Lei Zhang, Yan Liu, and David Zhang, Joint discriminative dimensionality reduction and dictionary learning for face recognition. To Appear in Pattern Recognition. (* contribute equally to this work).In addition the reviewer has serious concerns about the proposed approach:(1) Line 191-192, bi-linear optimization problem of the objective function in Eq. (5). Why is it bi-linear?(2) Convergence. Even though the authors show an example of convergence in practice, there is no guarantee because of the normalization of D. Consequently, the convergence of the method is highly dependent on the data, limiting the scalability of the method. Is it possible to analyze the convergence theoretically?(3) Classification. The proposed algorithm optimizes the variables D, P, and A alternatively in Eq (6). However, the proposed classification rule is based on Eq (5). Why don't you still use Eq (6) as your classification rule? That is, first estimate A for a test sample using Eq (8), and then checking the reconstruction error for each class as proposed. To me this is more consistent with what you optimize, and the computational cost is the same as the proposed one if pre-computing some matrices in Eq (8).(4) Line 306, robustness to variable m. I have my doubts about this statement. My line of thinking is as follows: This parameter essentially determines the rank of the matrix DP in Eq (5) explicitly. This actually is equivalent to controlling the model complexity by essentially enforcing low-rank constraints. If we carefully check the details in the experimental section, we can find that the value of this parameter is always much smaller than the dimensionality of features used in each dataset, which guarantees the low-rank property. So why don't you plot a figure that contains the classification accuracy with increasing m?