  In label-noise learning, estimating the transition matrix has attracted more
and more attention as the matrix plays an important role in building
statistically consistent classifiers. However, it is very challenging to
estimate the transition matrix T(x), where x denotes the instance, because it
is unidentifiable under the instance-dependent noise(IDN). To address this
problem, we have noticed that, there are psychological and physiological
evidences showing that we humans are more likely to annotate instances of
similar appearances to the same classes, and thus poor-quality or ambiguous
instances of similar appearances are easier to be mislabeled to the correlated
or same noisy classes. Therefore, we propose assumption on the geometry of T(x)
that "the closer two instances are, the more similar their corresponding
transition matrices should be". More specifically, we formulate above
assumption into the manifold embedding, to effectively reduce the degree of
freedom of T(x) and make it stably estimable in practice. The proposed
manifold-regularized technique works by directly reducing the estimation error
without hurting the approximation error about the estimation problem of T(x).
Experimental evaluations on four synthetic and two real-world datasets
demonstrate that our method is superior to state-of-the-art approaches for
label-noise learning under the challenging IDN.
