  Noisy labels can impair the performance of deep neural networks. To tackle
this problem, in this paper, we propose a new method for filtering label noise.
Unlike most existing methods relying on the posterior probability of a noisy
classifier, we focus on the much richer spatial behavior of data in the latent
representational space. By leveraging the high-order topological information of
data, we are able to collect most of the clean data and train a high-quality
model. Theoretically we prove that this topological approach is guaranteed to
collect the clean data with high probability. Empirical results show that our
method outperforms the state-of-the-arts and is robust to a broad spectrum of
noise types and levels.
