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

Abstract

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.

References in corpus (9)

• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Light fields in complex media: mesoscopic scattering meets wave control
• Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium
• Scalable Optical Learning Operator
• Filtering Random Matrices: The Effect of Incomplete Channel Control in Multiple Scattering
• Random Projections through multiple optical scattering: Approximating kernels at the speed of light
• Photonic extreme learning machine by free-space optical propagation
• Transmission eigenchannels and the densities of states of random media
• Disordered Anderson Localization Optical Fibers for Image Transport - A Review

Cited by in corpus (2)

• The Goldilocks Principle of Learning Unitaries by Interlacing Fixed Operators with Programmable Phase Shifters on a Photonic Chip
• Integrated Photonic Programmable Random Matrix Generator with Minimal Active Components