Related papers: Persistence Diagrams with Linear Machine Learning …
Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…
Recognition of occluded objects in unseen indoor environments is a challenging problem for mobile robots. This work proposes a new slicing-based topological descriptor that captures the 3D shape of object point clouds to address this…
Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Popular network models such as the mixed membership and standard stochastic block model are known to exhibit distinct geometric structure when embedded into $\mathbb{R}^{d}$ using spectral methods. The resulting point cloud concentrates…
In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs.…
Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…
Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a…
Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
In the realm of image processing and computer vision (CV), machine learning (ML) architectures are widely applied. Convolutional neural networks (CNNs) solve a wide range of image processing issues and can solve image compression problem.…
Image and Point Clouds provide different information for robots. Finding the correspondences between data from different sensors is crucial for various tasks such as localization, mapping, and navigation. Learning-based descriptors have…
The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a…
Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…