Related papers: ATOL: Measure Vectorization for Automatic Topologi…

Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…

Ordering has been extensively studied in many visualization applications, such as axis and matrix reordering, for the simple reason that the order will greatly impact the perceived pattern of data. Many quality metrics concerning data…

Estimating the region of attraction (${\tt RoA}$) for a robot controller is essential for safe application and controller composition. Many existing methods require a closed-form expression that limit applicability to data-driven…

We use Topological Data Analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify lifetime of…

This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…

Active Learning has received significant attention in the field of machine learning for its potential in selecting the most informative samples for labeling, thereby reducing data annotation costs. However, we show that the reported lifts…

Automated axon tracing via fully supervised learning requires large amounts of 3D brain imagery, which is time consuming and laborious to obtain. It also requires expertise. Thus, there is a need for more efficient segmentation and…

In artificial-intelligence-aided signal processing, existing deep learning models often exhibit a black-box structure, and their validity and comprehensibility remain elusive. The integration of topological methods, despite its relatively…

Detecting anomalies in datasets is a longstanding problem in machine learning. In this context, anomalies are defined as a sample that significantly deviates from the remaining data. Meanwhile, optimal transport (OT) is a field of…

Inference of the network structure (e.g., routing topology) and dynamics (e.g., link performance) is an essential component in many network design and management tasks. In this paper we propose a new, general framework for analyzing and…

This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of…

Training data are usually limited or heterogeneous in many chemical and biological applications. Existing machine learning models for chemistry and materials science fail to consider generalizing beyond training domains. In this article, we…

Autonomous service mobile robots need to consistently, accurately, and robustly localize in human environments despite changes to such environments over time. Episodic non-Markov Localization addresses the challenge of localization in such…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…

In this paper we present a maneuver regulation scheme for Vertical Take-Off and Landing (VTOL) micro aerial vehicles (MAV). Differently from standard trajectory tracking, maneuver regulation has an intrinsic robustness due to the fact that…

Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite…

Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…

Introducing accelerated reconstruction algorithms into clinical settings requires measures of uncertainty quantification that accurately assess the relevant uncertainty introduced by the reconstruction algorithm. Many currently deployed…

This study proposes an anomaly detection method based on the Transformer architecture with integrated multiscale feature perception, aiming to address the limitations of temporal modeling and scale-aware feature representation in cloud…