Figure 1. The different forms of feature reconstructions to assess two feature spaces (blue and pink) describing the same dataset.

Here, we are reconstructing the curved manifold (blue) using the planar manifold (pink), as it is often the case to approximate a complex manifold with a simpler alternative. The area framed by the dotted line is an example of a local neighbourhood of one sample (the pink dot) that enables the reconstruction of nonlinearities. (Top) The linear transformation is used in the global feature reconstruction error (GFRE). (Middle) The orthogonal transformation is used in the global feature reconstruction distortion (GFRD). (Bottom) A local linear transformation of a neighbourhood is used in local feature reconstruction error (LFRE). On the right, the reconstructions of the manifold are drawn in pink together with the curved manifold in blue. The measures correspond to the root-mean-square difference between the reconstructed and curved manifold.