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.

研究了标签噪声学习问题中的转移矩阵估计，基于人类任务标注时更加倾向于将外观相似的实例标注为同一类别的心理学和生理学证据，提出了T（x）几何形状的假设，并利用流形嵌入技术来有效地减少了其自由度并使其在实践中稳定可估计。实验结果表明，该方法在处理具有挑战性IDN数据时优于现有方法。

流形正则化过渡矩阵估计下的实例相关标签噪声学习