Related papers: Tree-Wasserstein Distance for High Dimensional Dat…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…

To address the computational and storage challenges posed by large-scale datasets in deep learning, dataset distillation has been proposed to synthesize a compact dataset that replaces the original while maintaining comparable model…

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be…

Detecting tiny objects is a very challenging problem since a tiny object only contains a few pixels in size. We demonstrate that state-of-the-art detectors do not produce satisfactory results on tiny objects due to the lack of appearance…

Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new…

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…

Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…

Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability…

A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…

Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space $(X,…

Deep unfolding networks have gained increasing attention in the field of compressed sensing (CS) owing to their theoretical interpretability and superior reconstruction performance. However, most existing deep unfolding methods often face…

Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute…

Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics…