UMS

Re-synthesis of from using UMS (Section 3.3) is done as follows. Given a fixed feature value , the manifold is given by Any that meets the first requirement can be written

where and where is the ortho-normal matrix that spans the linear subspace orthogonal to the columns of . Thus, spans the manifold. To satisfy the second requirement, we need Thus, we need the vector to have length Thus, lies on a hyper-sphere. Uniformly sampling a hyper-sphere is accomplished by drawing as iid samples of zero-mean Gaussian random variable, then normalizing to have length equal to the hyper-sphere radius. This works because the multivariate standard Gaussian has a distribution that projects evenly anywhere on the standard hyper-sphere. In summary, the sampling method is: (1) Draw a sample , samples of independent Gaussian samples of mean 0 and variance 1, (2) Let then (3) Let For more information see the function software/module_lin_gauss_synth.m.

Baggenstoss 2017-05-19