  Extracting noisy or incorrectly labeled samples from a labeled dataset with
hard/difficult samples is an important yet under-explored topic. Two general
and often independent lines of work exist, one focuses on addressing noisy
labels, and another deals with hard samples. However, when both types of data
are present, most existing methods treat them equally, which results in a
decline in the overall performance of the model. In this paper, we first design
various synthetic datasets with custom hardness and noisiness levels for
different samples. Our proposed systematic empirical study enables us to better
understand the similarities and more importantly the differences between
hard-to-learn samples and incorrectly-labeled samples. These controlled
experiments pave the way for the development of methods that distinguish
between hard and noisy samples. Through our study, we introduce a simple yet
effective metric that filters out noisy-labeled samples while keeping the hard
samples. We study various data partitioning methods in the presence of label
noise and observe that filtering out noisy samples from hard samples with this
proposed metric results in the best datasets as evidenced by the high test
accuracy achieved after models are trained on the filtered datasets. We
demonstrate this for both our created synthetic datasets and for datasets with
real-world label noise. Furthermore, our proposed data partitioning method
significantly outperforms other methods when employed within a semi-supervised
learning framework.
