Random Projections with Transverse Disorder in Optical Waveguide Arrays

Random projection is an efficient method for dimensionality reduction when dealing with very high-dimensional data. In this technique, data are mapped linearly from a high-dimensional space to a low-dimensional subspace, while nearly preserving their Euclidean distances during this transformation. Here, we show that random projection can be performed optically, by propagating spatially modulated light in photonic lattices with transverse disorder and by random sampling at the waveguide outputs. This realization allows for the integrated photonic implementation of random projection. We show that proper implementation of random projection requires transverse diagonal disorder of a critical strength that ensures diffusive transport of light rather than ballistic or localized transport.