Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization.

Optimization is at the heart of machine learning, statistics, and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applicable and are particularly well-suited to nonsmooth, constrained, large-scale, and distributed optimization problems.

Self-Representation Based Unsupervised Exemplar Selection in a Union of Subspaces.

Finding a small set of representatives from an unlabeled dataset is a core problem in a broad range of applications such as dataset summarization and information extraction. Classical exemplar selection methods such as k-medoids work under the assumption that the data points are close to a few cluster centroids, and cannot handle the case where data lie close to a union of subspaces. This paper proposes a new exemplar selection model that searches for a subset that best reconstructs all data points as measured by the l norm of the representation coefficients.