  We propose and experimentally demonstrate a nonlinear-optics approach to
pattern recognition with single-pixel imaging and deep neural network. It
employs mode selective image up-conversion to project a raw image onto a set of
coherent spatial modes, whereby its signature features are extracted
nonlinear-optically. With 40 projection modes, the classification accuracy
reaches a high value of 99.49% for the MNIST handwritten digit images, and up
to 95.32% even when they are mixed with strong noise. Our experiment harnesses
rich coherent processes in nonlinear optics for efficient machine learning,
with potential applications in online classification of large size images, fast
lidar data analyses, complex pattern recognition, and so on.
