Distance Metric Learning: Foundation, Methods and Applications

Distance Metric Learning (DML) is a machine learning approach that aims to
learn a new distance metric from data, which improves the quality of the distance-based
methods including classification, clustering, dimension reduction, kernel-based techniques,
information (e.g. image) retrieval and computer vision. In case of supervised learning prob-
lems, the output of DML are embeddings, where the input data are mapped to improve a
crisp or fuzzy classification process. In other words, DML focuses on searching for a trans-
formation of the original space into a new Euclidean space, in which the distance of objects
belonging to the same class becomes smaller than the distance between objects belonging
to different classes.
This talk summarizes some of the recent developments in research and application of
the distance metric learning method. Each DML algorithm consists of two main parts:

(1) modelling the distance-based constrains in form of an optimisation problem from a given
data set, and

(2) proposing an efficient algorithm for solving the constructed in step (1)
optimisation problem. In this talk, an overview of modelling techniques for classification,
clustering and information retrieval tasks as well as the optimisation techniques including
convex optimisation, different variants of gradient descent (stochastic, projected, ...), Frank-
Wolfe algorithms or Bregman projection will be presented.
The lecture will also cover one of the latest research topics, which is Deep Distance Metric
Learning. The goal of this research is to design a deep neural network that would be able to
tell which objects in different images are visually similar and which are not? Therefore, the
deep distance metric learning approach is actually a DLM method implemented by using
deep neural networks. The advantage of such models is the discovery of highly representative
non-linear embeddings.
Finally, the perspectives of Distance Metric Learning topic and the challenges in the
near future for research and development will be presented.