Fig. 3: Non-linear principal component analysis (PCA) using distributed feedback.

a The raw dataset consisted of 500 3-dimensional points randomly distributed on 3 concentric spheres. The colors (blue, red, orange) indicate data points on the 3 different spheres with radii of 1, 2, or 3. b Linear PCA of the raw data fails to separate the 3 classes of points. Plotted are the weights of the first 2 principle components (PC) for each datapoint. c A random linear transform is similarly unable to separate the 3 classes of points. d After the application of a non-linear random projection using Rayleigh backscattering, the 3 classes are clearly separable using a standard PCA. e Result of a PCA applied to 3 speckle grains selected from the RBS pattern, showing that the classes are difficult to separate without expanding the dimensionality. f Result of a PCA applied after re-compressing the RBS speckle pattern into 3 dimensions using a low-pass filter.