Related papers: Efficient Cover Construction for Ball Mapper via A…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…
Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through "the middle" of data distribution. We propose an algorithm for fast construction of grid…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Motivation: High throughput DNA sequencing (HTS) technologies generate an excessive number of small DNA segments -- called short reads -- that cause significant computational burden. To analyze the entire genome, each of the billions of…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
This paper studies the problem of polygonal mapping of buildings by tackling the issue of mask reversibility that leads to a notable performance gap between the predicted masks and polygons from the learning-based methods. We addressed such…
Most of the existing point-to-mesh distance query solvers, such as Proximity Query Package (PQP), Embree and Fast Closest Point Query (FCPW), are based on bounding volume hierarchy (BVH). The hierarchical organizational structure enables…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
Mobile mapping, in particular, Mobile Lidar Scanning (MLS) is increasingly widespread to monitor and map urban scenes at city scale with unprecedented resolution and accuracy. The resulting point cloud sampling of the scene geometry can be…
We address the problems of measuring geometric similarity between 3D scenes, represented through point clouds or range data frames, and associating them. Our approach leverages macro-scale 3D structural geometry - the relative configuration…
This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions,…
We present Fast Approximate Minimum Spanning Tree (FAMST), a novel algorithm that addresses the computational challenges of constructing Minimum Spanning Trees (MSTs) for large-scale and high-dimensional datasets. FAMST utilizes a…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the Popularity$\times$Similarity…
The Topological Data Analysis Ball Mapper (TDABM) algorithm of Dlotko (2019) provides a model free means to visualize multi-dimensional data. The visualizations are abstract two-dimensional representations of covers of the dataset. To…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that…