  We provide a new interpretation of Hessian locally linear embedding (HLLE),
revealing that it is essentially a variant way to implement the same idea of
locally linear embedding (LLE). Based on the new interpretation, a substantial
simplification can be made, in which the idea of "Hessian" is replaced by
rather arbitrary weights. Moreover, we show by numerical examples that HLLE may
produce projection-like results when the dimension of the target space is
larger than that of the data manifold, and hence one further modification
concerning the manifold dimension is suggested. Combining all the observations,
we finally achieve a new LLE-type method, which is called tangential LLE
(TLLE). It is simpler and more robust than HLLE.
