Semi-supervised metric learning incorporating weighted triplet constraint and Riemannian manifold optimization for classification

Metric learning focuses on finding similarities between data and aims to enlarge the distance between the samples with different labels. This work proposes a semi-supervised metric learning method based on the point-to-class structure of the labeled data, which is computationally less expensive, especially than using point-to-point structure. Specifically, the point-to-class structure is formulated into a new triplet constraint, which could narrow the distance of inner-class data and enlarge the distance of inter-class data simultaneously. Moreover, for measuring dissimilarity between different classes, weights are introduced into the triplet constraint and forms the weighted triplet constraint. Then, two kinds of regularizers such as spatial regularizer are rationally incorporated respectively in this model to mitigate the overfitting phenomenon and preserve the topological structure of the data. Furthermore, Riemannian gradient descent algorithm is adopted to solve the proposed model, since it can fully exploit the geometric structure of Riemannian manifolds and the proposed model can be regarded as a generalization of the unconstrained optimization problem in Euclidean space on Riemannian manifold. By introducing such solution strategy, the variables are constrained to a specific Riemannian manifold in each step of the iterative solution process, thereby enabling efficient and accurate model resolution. Finally, we conduct classification experiments on various data sets and compare the classification performance to state-of-the-art methods. The experimental results demonstrate that our proposed method has better performance in classification, especially for hyperspectral image data.