Related papers: On the Stability of the Euler Characteristic Trans…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means…
Epigenetic Tracking (ET) is an Artificial Embryology system which allows for the evolution and development of large complex structures built from artificial cells. In terms of the number of cells, the complexity of the bodies generated with…
The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the…
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…
Deep learning has emerged as a technique of choice for rapid feature extraction across imaging disciplines, allowing rapid conversion of the data streams to spatial or spatiotemporal arrays of features of interest. However, applications of…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data…
Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology (and both are conjecturally isomorphic to a version of Heegaard…
The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…
Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference…
Topological features based on persistent homology capture high-order structural information so as to augment graph neural network methods. However, computing extended persistent homology summaries remains slow for large and dense graphs and…
Image segmentation is a fundamental topic in image processing and has been studied for many decades. Deep learning-based supervised segmentation models have achieved state-of-the-art performance but most of them are limited by using…
As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…
Triplet loss is widely used for learning local descriptors from image patch. However, triplet loss only minimizes the Euclidean distance between matching descriptors and maximizes that between the non-matching descriptors, which neglects…
Parameter-efficient finetuning (PEFT) has become ubiquitous to adapt foundation models to downstream task requirements while retaining their generalization ability. However, the amount of additionally introduced parameters and compute for…
The Persistent Homology Transform (PHT) summarizes a shape in $\mathbb{R}^m$ by collecting persistence diagrams obtained from linear height filtrations in all directions on $\mathbb{S}^{m-1}$. It enjoys strong theoretical guarantees,…
This paper adopts a tool from computational topology, the Euler characteristic curve (ECC) of a sample, to perform one- and two-sample goodness of fit tests. We call our procedure TopoTests. The presented tests work for samples of arbitrary…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
Dynamic graph-level embedding aims to capture structural evolution in networks, which is essential for modeling real-world scenarios. However, existing methods face two critical yet under-explored issues: Structural Visit Bias, where random…