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Random feature maps are ubiquitous in modern statistical machine learning,where they generalize random projections by means of powerful, yet oftendifficult to analyze nonlinear operators. In this paper, we leverage the"concentration" phenomenon induced by random matrix theory to perform aspectral analysis on the Gram matrix of these random feature maps, here forGaussian mixture models of simultaneously large dimension and size. Our resultsare instrumental to a deeper understanding on the interplay of the nonlinearityand the statistics of the data, thereby allowing for a better tuning of randomfeature-based techniques.

On the Spectrum of Random Features Maps of High Dimensional Data