Related papers: Geometric Aspects of Data-Processing of Markov Cha…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process model for transfer learning purposes. To achieve this goal,…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…

Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…

The purpose of this paper is to employ the language of Cartan moving frames to study the geometry of the data manifolds and its Riemannian structure, via the data information metric and its curvature at data points. Using this framework and…

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…

This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…

We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the…

A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…

Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…

Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to…

Ensuring proper generalization is a critical challenge in applying data-driven methods for solving inverse problems in imaging, as neural networks reconstructing an image must perform well across varied datasets and acquisition geometries.…

Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with…

We introduce a graph-theoretic approach to extract clusters and hierarchies in complex data-sets in an unsupervised and deterministic manner, without the use of any prior information. This is achieved by building topologically embedded…