Related papers: How Small Can Faithful Sets Be? Ordering Topologic…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Creating comprehensible visualizations of highly overlapping set-typed data is a challenging task due to its complexity. To facilitate insights into set connectivity and to leverage semantic relations between intersections, we propose a…
Descriptors play an important role in data-driven materials design. While most descriptors of crystalline materials emphasize structure and composition, they often neglect the electron density - a complex yet fundamental quantity that…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based…
This paper proposes a novel approach to semantic ontology alignment using contextual descriptors. A formalization was developed that enables the integration of essential and contextual descriptors to create a comprehensive knowledge model.…
Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric…
We study sets and groups definable in tame expansions of o-minimal structures. Let $\mathcal {\widetilde M}= \langle \mathcal M, P\rangle$ be an expansion of an o-minimal $\mathcal L$-structure $\cal M$ by a dense set $P$, such that three…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, which is essential for modeling anisotropic mechanical…
Covering-based rough set theory is a useful tool to deal with inexact, uncertain or vague knowledge in information systems. Topology, one of the most important subjects in mathematics, provides mathematical tools and interesting topics in…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
The Euler Characteristic Transform (ECT) has proven to be a powerful representation, combining geometrical and topological characteristics of shapes and graphs. However, the ECT was hitherto unable to learn task-specific representations. We…
The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or…
Embedding networks into a fixed dimensional feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors (graph descriptors) are used to measure the pairwise similarity…
A distinctive representation of image patches in form of features is a key component of many computer vision and robotics tasks, such as image matching, image retrieval, and visual localization. State-of-the-art descriptors, from…
In this study, we evaluate several classifiers and focus on selecting a minimal set of appropriate material features. Our objective is to propose and discuss general strategies for reducing the number of descriptors required for material…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
In this paper we present the methodology for detecting outliers and testing the goodness-of-fit of random sets using topological data analysis. We construct the filtration from level sets of the signed distance function and consider various…
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…