Related papers: Topological Metric for Unsupervised Embedding Qual…
Stance detection is an important task, supporting many downstream tasks such as discourse parsing and modeling the propagation of fake news, rumors, and science denial. In this paper, we propose a novel framework for stance detection. Our…
Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a…
Persistent homology, the study of holes that appear in data as one thickens balls centered around its points over time, has theoretically guaranteed stability. That is, small data perturbations guarantee small changes in the lifetimes of…
Self-supervised learning models extract general-purpose representations from data. Quantifying the reliability of these representations is crucial, as many downstream models rely on them as input for their own tasks. To this end, we…
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…
Spatial transcriptomics studies are becoming increasingly large and commonplace, necessitating simultaneous analysis of a large number of spatially resolved variables. Correspondingly, a diverse range of methodologies have been proposed to…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
The evaluation of recent embedding-based evaluation metrics for text generation is primarily based on measuring their correlation with human evaluations on standard benchmarks. However, these benchmarks are mostly from similar domains to…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
In recent years, topological data analysis has been utilized for a wide range of problems to deal with high dimensional noisy data. While text representations are often high dimensional and noisy, there are only a few work on the…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
Persistent homology (PH) has been widely applied to graph data to extract topological features. However, little attention has been paid to how different distance functions on a graph affect the resulting persistence barcodes and their…
Self-supervised learning (SSL) has great potential for molecular representation learning given the complexity of molecular graphs, the large amounts of unlabelled data available, the considerable cost of obtaining labels experimentally, and…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…