  The popular softmax loss and its recent extensions have achieved great
success in the deep learning-based image classification. However, the data for
training image classifiers usually has different quality. Ignoring such
problem, the correct classification of low quality data is hard to be solved.
In this paper, we discover the positive correlation between the feature norm of
an image and its quality through careful experiments on various applications
and various deep neural networks. Based on this finding, we propose a
contraction mapping function to compress the range of feature norms of training
images according to their quality and embed this contraction mapping function
into softmax loss or its extensions to produce novel learning objectives. The
experiments on various classification applications, including handwritten digit
recognition, lung nodule classification, face verification and face
recognition, demonstrate that the proposed approach is promising to effectively
deal with the problem of learning on the data with different quality and leads
to the significant and stable improvements in the classification accuracy.
