Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time we present a highly-scalable spectral approach (GRASPEL) for learning large graphs from data. By limiting the precision matrix to be a graph Laplacian, our approach aims to estimate ultra-sparse (tree-like) weighted undirected graphs and shows a clear connection with the prior graphical Lasso method. By interleaving the latest high-performance nearly-linear time spectral methods for graph sparsification, coarsening and embedding, ultra-sparse yet spectrally-robust graphs can be learned by identifying and including the most spectrally-critical edges into the graph. Compared with prior state-of-the-art graph learning approaches, GRASPEL is more scalable and allows substantially improving computing efficiency and solution quality of a variety of data mining and machine learning applications, such as spectral clustering (SC), and t-Distributed Stochastic Neighbor Embedding (t-SNE). For example, when comparing with graphs constructed using existing methods, GRASPEL achieved the best spectral clustering efficiency and accuracy.
In this paper, the authors present a method that transforms data into graph. They emphasize on the fact that the proposed method is scalable, using a spectral embedding to construct the graph.
We think that the paper is not of enough quality to be accepted in ICLR. Without going in detail in the derivations, we give below some major issues in this submitted paper.
The studied problem has been widely investigated in the literature. Many methods have been proposed within the same objective, including taking care of the scalability issue. The authors fail to provide the state of the art, as well as describe the contributions with respect to previous work. As a consequence, the contributions are not clear. Maybe the proposed framework is original, but the there has been plenty of methods that have considered the same problem.
Experiments are poor and not convincing. The authors compare the proposed method to only two spectral clustering methods, which as the standard kNN and the Consensus kNN from 2013. These two methods are pretty old and many more recent methods have been introduced in the literature. Moreover, the results in Table 1 are somehow misleading, as the standard kNN is faster that the proposed method on 3 out of 4 datasets. Experiments in graph recovery are not clear, starting from the fact that the datasets are not defined (what are the Gaussian graph and ER graph?), neither the experimental setting (what is the problem at hand?). The same goes to the application of t-SNE which is also very weak.
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Reply to Rebuttal 
The authors have modified the paper to take into consideration our previous comments and suggestions. However, we think that it is still of not sufficient quality. We give below some elements, without providing a thorough review.
It is pretty pretentious to say that "this is the first work that introduces a spectral method for learning ultra-sparse (tree-like) graphs from data", while not comparing to the state of the art. There have been many spectral methods in graph learning for large-scale datasets.
In experiments, the only added method is the one of Kalofolias and Perraudin (submitted in 2017 to ArXiv). However, results show that this method is the worst of all methods. It is even the worst compared to the simple standard knn. It is not clear how the authors get such results; It looks like something is wrong in experiments, or they are cherrypicking.