Semi-supervised Subspace Metric Learning

Metric learning is a popular approach for measuring the similarity between samples and is essential for many machine learning tasks. However, its performance may be degraded when the data is corrupted by noise, the feature is redundant, or the data is heterogeneously distributed. To circumvent these limitations, we propose a semi-supervised subspace local metric learning algorithm. Specifically, we find a low-dimensional subspace by regarding the subspace learning as an inverse problem on Grassmannian manifold. Then we learn some local positive definite metrics on the subspace defined on different regions and optimize them using intrinsic steep decent method. We also introduce a manifold regularizer to preserve the data geometric structure. At last, our experiments show that, even on noisy datasets, we still improve the accuracy and robustness compared with the state-of-the-art metric learning algorithms.