2017/09/18 by Lalit Jain, Jain, Lalit, Blake Mason +3 · 1 citation
Computer Science · Engineering · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (stat.ML) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1709.06171
openalex publication_date 2017/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy of the learned metric relative to the underlying true generative metric. All the results involve novel mathematical approaches to the metric learning problem, and lso shed new light on the special case of ordinal embedding (aka non-metric multidimensional scaling).