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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary: The authors provide a novel method for oblivious subspace embedding that is computationally efficient in a sense that it circumvents explicit computation of feature map. Essentially, what the authors suggest is a special way to do implicit low-rank approximation of feature matrix. Asymptotic properties of that approximation are also shown in the paper. The paper mostly focuses on feature map with polynomial kernel, leaving out infinite dimensional kernels for further research.