Abstract 

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the JohnsonLindenstrauss transform and the angular kernel, we show that we can select matrices yielding guaranteed improved performance in accuracy and/or speed compared to earlier methods. We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.