A Tutorial on Distance Metric Learning: Mathematical Foundations, Algorithms and Experiments

Distance metric learning is a branch of machine learning that aims to learn distances from the data. Distance metric learning can be useful to improve similarity learning algorithms, and also has applications in dimensionality reduction. This paper describes the distance metric learning problem and analyzes its main mathematical foundations. In addition, it also discusses some of the most popular distance metric learning techniques used in classification, showing their goals and the required information to understand and use them. Furthermore, some experiments to evaluate the performance of the different algorithms are also provided. Finally, this paper discusses several possibilities of future work in this topic.