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Assigning discriminable and harmonic colors to samples according to their class labels and spatial distribution can generate attractive visualizations and facilitate data exploration. However, as the number of classes increases, it is…
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…
Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…
In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally…
Given a set of detections, detected at each time instant independently, we investigate how to associate them across time. This is done by propagating labels on a set of graphs, each graph capturing how either the spatio-temporal or the…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Here a semi-implicit formulation of the gradient augmented level set method is presented. By tracking both the level set and it's gradient accurate subgrid information is provided,leading to highly accurate descriptions of a moving…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power…
The level set approach represents surfaces implicitly, and advects them by evolving a level set function, which is numerically defined on an Eulerian grid. Here we present an approach that augments the level set function values by gradient…
In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions.…
Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper, they proposed a rankability measure that is based on a…
We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based…
An adjacency labeling scheme is a method that assigns labels to the vertices of a graph such that adjacency between vertices can be inferred directly from the assigned label, without using a centralized data structure. We devise adjacency…
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…
We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…
Given a sample from a probability measure with support on a submanifold in Euclidean space one can construct a neighborhood graph which can be seen as an approximation of the submanifold. The graph Laplacian of such a graph is used in…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
Label propagation is a powerful and flexible semi-supervised learning technique on graphs. Neural networks, on the other hand, have proven track records in many supervised learning tasks. In this work, we propose a training framework with a…