Related papers: Calibrated Persistent Homology Tests for High-dime…
This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to…
In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in Euclidean space given by image. Carlsson et al. proposed a…
Spontaneous collapse models aim to solve the long-standing measurement problem in quantum mechanics by modifying the theory's dynamics to include objective wave function collapses. These collapses occur randomly in space, bridging the gap…
A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time.…
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…
Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for…
Computer model calibration involves using partial and imperfect observations of the real world to learn which values of a model's input parameters lead to outputs that are consistent with real-world observations. When calibrating models…
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
Dynamically significant magnetic fields are routinely observed in molecular clouds, with mass-to-flux ratio lambda = (2 pi sqrt{G}) (Sigma/B) ~ 1 (here Sigma is the total column density and B is the field strength). It is widely believed…
Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with…
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensional persistence modules and…
Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based…
We propose a novel clustering approach for point-cloud segmentation based on supervised contrastive metric learning (CML). Rather than predicting cluster assignments or object-centric variables, the method learns a latent representation in…
We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…
The nature of stacking faults - whether intrinsic or extrinsic - plays a pivotal role in defect-mediated processes in crystalline materials. Yet, current electron microscopy techniques for their reliable analysis remain limited to either…
Large-scale coherent structures are identified in turbulent pipe flow at $Re_\tau=181$ by having long lifetimes, living on large scales and travelling with a certain group velocity. A Characteristic Dynamic Mode Decomposition (CDMD) is used…
We show that recent results on randomized dimension reduction schemes that exploit structural properties of data can be applied in the context of persistent homology. In the spirit of compressed sensing, the dimension reduction is…
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…