Related papers: Multiscale Geometric Methods for Data Sets II: Geo…
A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
An effective 3D descriptor should be invariant to different geometric transformations, such as scale and rotation, robust to occlusions and clutter, and capable of generalising to different application domains. We present a simple yet…
Point cloud stands as the most widely adopted format for representing 3D shapes and scenes due to its simplicity and geometric fidelity. However, its inherent unordered and irregular nature, exacerbated by sensor noise and occlusions,…
Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…
Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
Point cloud compression plays a crucial role in reducing the huge cost of data storage and transmission. However, distortions can be introduced into the decompressed point clouds due to quantization. In this paper, we propose a novel…
The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes,…
LiDAR sensors are an integral part of modern autonomous vehicles as they provide an accurate, high-resolution 3D representation of the vehicle's surroundings. However, it is computationally difficult to make use of the ever-increasing…
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…
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…
As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era,…
Building Information Modeling (BIM) technology is a key component of modern construction engineering and project management workflows. As-is BIM models that represent the spatial reality of a project site can offer crucial information to…
Semantic segmentation of 3D point cloud is an essential task for autonomous driving environment perception. The pipeline of most pointwise point cloud semantic segmentation methods includes points sampling, neighbor searching, feature…
We design the first learned index that solves the dictionary problem with time and space complexity provably better than classic data structures for hierarchical memories, such as B-trees, and modern learned indexes. We call our solution…
Vector-space word representations obtained from neural network models have been shown to enable semantic operations based on vector arithmetic. In this paper, we explore the existence of similar information on vector representations of…
Hyperdimensional (HD) computing is built upon its unique data type referred to as hypervectors. The dimension of these hypervectors is typically in the range of tens of thousands. Proposed to solve cognitive tasks, HD computing aims at…
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…
Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…