Linear Distance Metric Learning with Noisy Labels
This work addresses metric learning with noisy labels, offering theoretical guarantees and practical improvements, but it is incremental as it builds on existing linear metric learning frameworks.
The paper tackles the problem of learning a linear distance metric from data with noisy labels, showing that the ground truth metric can be learned with any precision given enough samples and providing a sample complexity bound. It also presents a method to truncate the learned model to low-rank while maintaining accuracy, supported by experiments on synthetic and real data.
In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible. In this paper, we formalize a simple and elegant method which reduces to a general continuous convex loss optimization problem, and for different noise models we derive the corresponding loss functions. We show that even if the data is noisy, the ground truth linear metric can be learned with any precision provided access to enough samples, and we provide a corresponding sample complexity bound. Moreover, we present an effective way to truncate the learned model to a low-rank model that can provably maintain the accuracy in loss function and in parameters -- the first such results of this type. Several experimental observations on synthetic and real data sets support and inform our theoretical results.