Mathematical derivation of LocalGaussian computation for Manifold Parzen, and errata

The aim of this report is to correct an inconsistency in the mathematical formulas thatappearedinourpreviouslypublishedManifoldParzenarticle(1), regardingthe computation of the density of "oriented" high dimensional Gaussian "pancakes" for which we store only the first d leading eigenvectors and eigenvalues (rather than a full n ◊ n covariance matrix, or its inverse). We give a detailed derivation leading to the correct formulas.