  Nonlinear embedding manifold learning methods provide invaluable visual
insights into the structure of high-dimensional data. However, due to a
complicated nonconvex objective function, these methods can easily get stuck in
local minima and their embedding quality can be poor. We propose a natural
extension to several manifold learning methods aimed at identifying pressured
points, i.e. points stuck in poor local minima and have poor embedding quality.
We show that the objective function can be decreased by temporarily allowing
these points to make use of an extra dimension in the embedding space. Our
method is able to improve the objective function value of existing methods even
after they get stuck in a poor local minimum.
