Online Low-Rank Metric Learning via Parallel Coordinate Descent Method

11The corresponding author is Prof. Yang Cong. This work is supported by Nature Science Foundation of China under Grant (61722311, U1613214, 61533015) and CAS-Youth Innovation Promotion Association Scholarship (2012163)Recently, many machine learning problems rely on a valuable tool: metric learning. However, in many applications, large-scale applications embedded in high-dimensional feature space may induce both computation and storage requirements to grow quadratically. In order to tackle these challenges, in this paper, we intend to establish a robust metric learning formulation with the expectation that online metric learning and parallel optimization can solve large-scale and high-dimensional data efficiently, respectively. Specifically, based on the matrix factorization strategy, the first step aims to learn a similarity function in the objective formulation for similarity measurement; in the second step, we derive a variational trace norm to promote low-rankness on the transformation matrix. After converting this variational regularization into its separable form, for the model optimization, we present an parallel block coordinate descent method to learn the optimal metric parameters, which can handle the high-dimensional data in an efficient way. Crucially, our method shares the efficiency and flexibility of block coordinate descent method, and it is also guaranteed to converge to the optimal solution. Finally, we evaluate our approach by analyzing scene categorization dataset with tens of thousands of dimensions, and the experimental results show the effectiveness of our proposed model.