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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The authors present an efficient method for dimensionality reduction which preserves subspace independence and, as consequence, is useful for problems such as classification where we assume that the data are separable on a lower-dimensional subspace. They show that the subspace structure preservation can be achieved with 2K projects, and they perform a detailed comparison with other methods on benchmark data. The paper is very thorough and well-presented. It presents a novel and effective method for an important problem in dimensionality reduction, and it does so in a way that makes it clear that the method is competitive with popular alternatives.