Instance-Dependent Label-Noise Learning with Manifold-Regularized Transition Matrix Estimation

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.