Support Regularized Sparse Coding and Its Fast Encoder
Sparse coding represents a signal by a linear combination of only a few atoms of a learned over-complete dictionary. While sparse coding exhibits compelling performance for various machine learning tasks, the process of obtaining sparse code with fixed dictionary is independent for each data point without considering the geometric information and manifold structure of the entire data. We propose Support Regularized Sparse Coding (SRSC) which produces sparse codes that account for the manifold structure of the data by encouraging nearby data in the manifold to choose similar dictionary atoms. In this way, the obtained support regularized sparse codes capture the locally linear structure of the data manifold and enjoy robustness to data noise. We present the optimization algorithm of SRSC with theoretical guarantee for the optimization over the sparse codes. We also propose a feed-forward neural network termed Deep Support Regularized Sparse Coding (Deep-SRSC) as a fast encoder to approximate the sparse codes generated by SRSC. Extensive experimental results demonstrate the effectiveness of SRSC and Deep-SRSC.
In this paper the authors propose a method to explicitly regularize sparse coding to encode neighbouring datapoints with similar sets of atoms from the dictionary by clustering training examples with KNN in input space. The resulting algorithm is relatively complex and computationally relatively expensive, but the authors provide detailed derivations and use arguments from proximal gradient descent methods to prove convergence (I did not follow all the derivations, only some). In general the paper is well written and the authors explain the motivation behind the algorithms design in detail. In the abstract the authors mention “extensive experimental results …”, but I find the experiments not very convincing: With experiments on the USPS handwritten digits dataset (why not MNIST?), COIL-20 and COIL-100 and UCI, the datasets are all relatively small and the algorithm is run with dictionary sizes between p=100 to p=500. This seems surprising because the authors state that they implemented SRSC in “CUDA C++ with extreme efficiency” (page 10). But more importantly, I find it hard to interpret and compare the results: The paper reports accuracy and and normalized mutual information for a image retrieval / clustering task where the proposed SRSC is used as a feature extractor. The improvements relative to standard Sparse Coding seem very small (often < 1% in terms of NMI; it looks more promising in terms of accuracy) and if I understand the description on page 11 correctly, than the test set was used to select some hyperparameters (the best similarity measure for clustering step)? There is no comparisons to other baselines / state of the art image clustering methods. Besides of providing features for a small scale image clustering system, are there maybe ways to more directly evaluate the properties and qualities of a sparse coding approach? E.g. reconstruction error / sparsity; maybe even denoising performance? In summary, I think in it current form the paper lacks the evaluation and experimental results for an ICLR publication. Intuitively, I agree with the authors that the proposed regularization is an interesting direction, but I don’t see experiments that directly show that the regularization has the desired effect; and the improvements in the clustering task where SRSC is used as a feature extractor are very modest.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Support Regularized Sparse Coding and Its Fast Encoder
Sparse coding represents a signal by a linear combination of only a few atoms of a learned over-complete dictionary. While sparse coding exhibits compelling performance for various machine learning tasks, the process of obtaining sparse code with fixed dictionary is independent for each data point without considering the geometric information and manifold structure of the entire data. We propose Support Regularized Sparse Coding (SRSC) which produces sparse codes that account for the manifold structure of the data by encouraging nearby data in the manifold to choose similar dictionary atoms. In this way, the obtained support regularized sparse codes capture the locally linear structure of the data manifold and enjoy robustness to data noise. We present the optimization algorithm of SRSC with theoretical guarantee for the optimization over the sparse codes. We also propose a feed-forward neural network termed Deep Support Regularized Sparse Coding (Deep-SRSC) as a fast encoder to approximate the sparse codes generated by SRSC. Extensive experimental results demonstrate the effectiveness of SRSC and Deep-SRSC.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



In this paper the authors propose a method to explicitly regularize sparse coding to encode neighbouring datapoints with similar sets of atoms from the dictionary by clustering training examples with KNN in input space. The resulting algorithm is relatively complex and computationally relatively expensive, but the authors provide detailed derivations and use arguments from proximal gradient descent methods to prove convergence (I did not follow all the derivations, only some). In general the paper is well written and the authors explain the motivation behind the algorithms design in detail. In the abstract the authors mention “extensive experimental results …”, but I find the experiments not very convincing: With experiments on the USPS handwritten digits dataset (why not MNIST?), COIL-20 and COIL-100 and UCI, the datasets are all relatively small and the algorithm is run with dictionary sizes between p=100 to p=500. This seems surprising because the authors state that they implemented SRSC in “CUDA C++ with extreme efficiency” (page 10). But more importantly, I find it hard to interpret and compare the results: The paper reports accuracy and and normalized mutual information for a image retrieval / clustering task where the proposed SRSC is used as a feature extractor. The improvements relative to standard Sparse Coding seem very small (often < 1% in terms of NMI; it looks more promising in terms of accuracy) and if I understand the description on page 11 correctly, than the test set was used to select some hyperparameters (the best similarity measure for clustering step)? There is no comparisons to other baselines / state of the art image clustering methods. Besides of providing features for a small scale image clustering system, are there maybe ways to more directly evaluate the properties and qualities of a sparse coding approach? E.g. reconstruction error / sparsity; maybe even denoising performance? In summary, I think in it current form the paper lacks the evaluation and experimental results for an ICLR publication. Intuitively, I agree with the authors that the proposed regularization is an interesting direction, but I don’t see experiments that directly show that the regularization has the desired effect; and the improvements in the clustering task where SRSC is used as a feature extractor are very modest.
assistant
In this paper the authors propose a method to explicitly regularize sparse coding to encode neighbouring datapoints with similar sets of atoms from the dictionary by clustering training examples with KNN in input space. The resulting algorithm is relatively complex and computationally relatively expensive, but the authors provide detailed derivations and use arguments from proximal gradient descent methods to prove convergence (I did not follow all the derivations, only some). In general the paper is well written and the authors explain the motivation behind the algorithms design in detail. In the abstract the authors mention “extensive experimental results …”, but I find the experiments not very convincing: With experiments on the USPS handwritten digits dataset (why not MNIST? ), COIL-20 and COIL-100 and UCI, the datasets are all relatively small and the algorithm is run with dictionary sizes between p=100 to p=500. This seems surprising because the authors state that they implemented SRSC in “CUDA C++ with extreme efficiency” (page 10). But more importantly, I find it hard to interpret and compare the results: The paper reports accuracy and and normalized mutual information for a image retrieval / clustering task where the proposed SRSC is used as a feature extractor. The improvements relative to standard Sparse Coding seem very small (often < 1% in terms of NMI; it looks more promising in terms of accuracy) and if I understand the description on page 11 correctly, than the test set was used to select some hyperparameters (the best similarity measure for clustering step)? There is no comparisons to other baselines / state of the art image clustering methods. Besides of providing features for a small scale image clustering system, are there maybe ways to more directly evaluate the properties and qualities of a sparse coding approach? E.g. reconstruction error / sparsity; maybe even denoising performance? In summary, I think in it current form the paper lacks the evaluation and experimental results for an ICLR publication. Intuitively, I agree with the authors that the proposed regularization is an interesting direction, but I don’t see experiments that directly show that the regularization has the desired effect; and the improvements in the clustering task where SRSC is used as a feature extractor are very modest.