相关论文: Pairwise Distance-Diffusion Analysis (PDDA): A Geo…

Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically…

Recent studies demonstrate that diffusion planners benefit from sparse-step planning over single-step planning. Training models to skip steps in their trajectories helps capture long-term dependencies without additional memory or…

We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and…

This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…

We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances…

High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an…

The pair-contact process with diffusion (PCPD), a generalized model of the ordinary pair-contact process (PCP) without diffusion, exhibits a continuous absorbing phase transition. Unlike the PCP, whose nature of phase transition is clearly…

The discrete-dipole approximation (DDA) is a flexible technique for computing scattering and absorption by targets of arbitrary geometry. In this paper we perform systematic study of various non-stationary iterative (conjugate gradient)…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, $H$. Specifically, DFA quantifies the…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…

Linear discriminant analysis improves class separability but struggles with non-linearly separable data. To overcome this, we introduce Deep Discriminant Analysis (DDA), which directly optimizes the Fisher criterion utilizing deep networks.…

Diffusion-based motion planners are becoming popular due to their well-established performance improvements, stemming from sample diversity and the ease of incorporating new constraints directly during inference. However, a primary…

Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…

Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

In this work, we design, analyze, and optimize sequential and shared-memory parallel algorithms for partitioned local depths (PaLD). Given a set of data points and pairwise distances, PaLD is a method for identifying strength of pairwise…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…