Nonlinear barycentric dimensionality reduction

Many high-dimensional datasets can be mapped onto lower-dimensional linear simplexes, parametrized by barycentric coordinates. We present an unsupervised algorithm that is able to find the barycentric coordinates and corresponding vertices of such a high-dimensional dataset, by combining manifold learning with a distance geometry based algorithm for finding a maximal volume inscribed simplex. The performance of the algorithm is demonstrated on a Swiss-roll dataset that is restricted to a simplex, and on the spectral unmixing of hyperspectral imagery.