  Convolutional neural network (CNN)-based feature learning has become state of
the art, since given sufficient training data, CNN can significantly outperform
traditional methods for various classification tasks. However, feature learning
becomes more difficult if some training labels are noisy. With traditional
regularization techniques, CNN often overfits to the noisy training labels,
resulting in sub-par classification performance. In this paper, we propose a
robust binary classifier, based on CNNs, to learn deep metric functions, which
are then used to construct an optimal underlying graph structure used to clean
noisy labels via graph Laplacian regularization (GLR). GLR is posed as a convex
maximum a posteriori (MAP) problem solved via convex quadratic programming
(QP). To penalize samples around the decision boundary, we propose two
regularized loss functions for semi-supervised learning. The binary
classification experiments on three datasets, varying in number and type of
features, demonstrate that given a noisy training dataset, our proposed
networks outperform several state-of-the-art classifiers, including label-noise
robust support vector machine, CNNs with three different robust loss functions,
model-based GLR, and dynamic graph CNN classifiers.
