Figure 1
From: Cost function for low-dimensional manifold topology assessment
Illustrative demonstration of non-uniqueness introduced during low-dimensional data projection. Various 2D projections of a 3D synthetic dataset can be formed by looking at the dataset at various angles to the z-axis and collapsing all observations onto a plane of sight. We demonstrate two example projections that can be formed: a top-down projection and a projection resulting from looking at an angle to the z-axis. In the new projected coordinates, \([\eta _1, \eta _2]\), the top-down projection is unique everywhere, while the projection at an angle introduces regions of non-uniqueness with overlapping observations.
