We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show
that it is well-posed in the limit of finite labeled data and infinite unlabeled data. In particular …

We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled
data and finite labeled data. Previous work has conjectured that Lipschitz learning is well …

Shortest path graph distances are widely used in data science and machine learning, since
they can approximate the underlying geodesic distance on the data manifold. However, the …

In multi-/many-objective evolutionary algorithms (MOEAs), there are varieties of vector
ranking schemes, including nondominated sorting, dominance counting, and so on. Usually …

Most content-based image retrieval systems consider either one single query, or multiple
queries that include the same object or represent the same semantic information. In this …

We consider the problem of identifying patterns in a data set that exhibits anomalous
behavior, often referred to as anomaly detection. Similarity-based anomaly detection …

We show that nondominated sorting of a sequence X_1,\dots,X_n of independent and
identically distributed random variables in R^d has a continuum limit that corresponds to …

We prove that a directed last passage percolation model with discontinuous macroscopic
(non-random) inhomogeneities has a continuum limit that corresponds to solving a Hamilton …

Nondominated sorting, also called Pareto depth analysis (PDA), is widely used in
multiobjective optimization and has recently found important applications in multicriteria …

Nondominated sorting is a discrete process that sorts points in Euclidean space according to
the coordinatewise partial order and is used to rank feasible solutions to multiobjective …