Bilevel Distance Metric Learning for Robust Image Recognition
Metric learning, aiming to learn a discriminative Mahalanobis distance matrix M that can effectively reflect the similarity between data samples, has been widely studied in various image recognition problems. Most of the existing metric learning methods input the features extracted directly from the original data in the preprocess phase. What's worse, these features usually take no consideration of the local geometrical structure of the data and the noise that exists in the data, thus they may not be optimal for the subsequent metric learning task. In this paper, we integrate both feature extraction and metric learning into one joint optimization framework and propose a new bilevel distance metric learning model. Specifically, the lower level characterizes the intrinsic data structure using graph regularized sparse coefficients, while the upper level forces the data samples from the same class to be close to each other and pushes those from different classes far away. In addition, leveraging the KKT conditions and the alternating direction method (ADM), we derive an efficient algorithm to solve the proposed new model. Extensive experiments on various occluded datasets demonstrate the effectiveness and robustness of our method.
Summary: The authors propose a bilevel method for metric learning, where the lower level is responsible for the extraction of discriminative features from the data based on a sparse coding scheme with graph regularization. This effectively detects their underlying geometric structure, and the upper level is a classic metric learning approach that utilizes the learned sparse coefficients. These two components are integrated into a joint optimization problem and an efficient optimization algorithm is developed accordingly. Hence, new data can be classified based on the learned dictionary and the corresponding metric. In the experiments the authors demonstrate the capabilities of the model to provide more discriminative features from high dimensional data, while being more robust to noise.  Quality: The technical contribution of the paper seems to be pretty solid. In particular, the argumentation about the feature extraction and why this is beneficial for the metric learning, is pretty convincing. Also, the final objective function is directly interpretable. In addition, the derivation of the optimization algorithm is as clean as possible, and nicely presented. Furthermore, the converge analysis of the algorithm is discussed as well. So the proposed framework is sufficiently complete. However, I have two comments:  1) The graph regularizer in Eq.16 utilizes the weights q_i, which are not defined properly in the text. Especially, given that the Laplacian is constructed during training in a supervised way.   2) Could you provide some information considering the efficiency of the model? Consider for instance the training time.  Clarity: The paper is very well-written and nicely organized. Also, it provides neatly all the necessary information to the reader. The related work seems to be discussed properly. I have few minor comments:  1) In Fig.1 it would be nice if you could give a better explanation of the x-axis. To my undestanding these are the samples i=1,...n categorized, but this is not direcly communicated by the figure.   2) Does the construction of the Laplacian in a supervised way implies that you construct the adjacency matrix based on the given labels?  3) In Fig.2 you could have used log-scale for the y-axis.  Originality: I am not an expert in the field, but the related work seems to be properly cited. Also, by taking into account the related work as presented by the authors, the proposed model seems to be novel enough. Even if the bilevel concept with the graph regularized sparse coding as an integrated feature extractor has been utilized in previous models, in the current paper it is considered into the metric learning framework. Also, the provided optimization algorithm has been developed specifically for the proposed model.   Significance: The idea of integrating a meaningful feature extractor in the metric learning task, is very interesting and makes a lot of sense. Especially, I like the fact that in the proposed model this combination is implemented naturally. Also, the developed optimization algorithm is remarkable, since it solves a rather complicated problem. The improvement upon the results of the experiments is considerable, which shows that the proposed approach is particularly useful.   General comments: The general idea of bilevel models is pretty appealing. In particular, the lower level is designed in such a way that it provides meaningful features into the upper level, which solves the main problem. In this paper, the discriminative features that capture the underlying geometric structure of the data are utilized such that to learn a Mahalanobis distance for classification. The provided optimization algorithm that solves the joint problem is very interesting as well, since the problem is challenging. The experimental results show that, indeed, extracting meaningful features from the data, can lead to significant improvements.   ------------------------------------------------ After reading the rebuttal my final comments are that the submission seems to be solid, and also, considering the replies of the authors, I feel that they answer sufficiently well all the comments of the reviewers. So I will keep my score and vote for acceptance.