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It is proposed that the propagation of light in disordered photonic latticescan be harnessed as a random projection that preserves distances between a setof projected vectors. This mapping is enabled by the complex evolution matrixof a photonic lattice with diagonal disorder, which turns out to be a randomcomplex Gaussian matrix. Thus, by collecting the output light from a subset ofthe waveguide channels, one can perform an embedding from a higher-dimension toa lower-dimension space that respects the Johnson-Lindenstrauss lemma andnearly preserves the Euclidean distances. It is discussed thatdistance-preserving random projection through photonic lattices requiresintermediate disorder levels that allow diffusive spreading of light from asingle channel excitation, as opposed to strong disorder which initiates thelocalization regime. The proposed scheme can be utilized as a simple andpowerful integrated dimension reduction stage that can greatly reduce theburden of a subsequent neural computing stage.

Integrated Random Projection and Dimensionality Reduction by Propagating Light in Photonic Lattices