  Traditional manifold learning algorithms assumed that the embedded manifold
is globally or locally isometric to Euclidean space. Under this assumption,
they divided manifold into a set of overlapping local patches which are locally
isometric to linear subsets of Euclidean space. By analyzing the global or
local isometry assumptions it can be shown that the learnt manifold is a flat
manifold with zero Riemannian curvature tensor. In general, manifolds may not
satisfy these hypotheses. One major limitation of traditional manifold learning
is that it does not consider the curvature information of manifold. In order to
remove these limitations, we present our curvature-aware manifold learning
algorithm called CAML. The purpose of our algorithm is to break the local
isometry assumption and to reduce the dimension of the general manifold which
is not isometric to Euclidean space. Thus, our method adds the curvature
information to the process of manifold learning. The experiments have shown
that our method CAML is more stable than other manifold learning algorithms by
comparing the neighborhood preserving ratios.
