  It is proposed that the propagation of light in disordered photonic lattices
can be harnessed as a random projection that preserves distances between a set
of projected vectors. This mapping is enabled by the complex evolution matrix
of a photonic lattice with diagonal disorder, which turns out to be a random
complex Gaussian matrix. Thus, by collecting the output light from a subset of
the waveguide channels, one can perform an embedding from a higher-dimension to
a lower-dimension space that respects the Johnson-Lindenstrauss lemma and
nearly preserves the Euclidean distances. It is discussed that
distance-preserving random projection through photonic lattices requires
intermediate disorder levels that allow diffusive spreading of light from a
single channel excitation, as opposed to strong disorder which initiates the
localization regime. The proposed scheme can be utilized as a simple and
powerful integrated dimension reduction stage that can greatly reduce the
burden of a subsequent neural computing stage.
