Related papers: Topological Data Analysis with $\epsilon$-net Indu…
In this study, we explore the impact of network topology on the approximation capabilities of artificial neural networks (ANNs), with a particular focus on complex topologies. We propose a novel methodology for constructing complex ANNs…
Image landmark detection aims to automatically identify the locations of predefined fiducial points. Despite recent success in this field, higher-ordered structural modeling to capture implicit or explicit relationships among anatomical…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing…
Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…
Point clouds are widely used representations of 3D data, but determining the visibility of points from a given viewpoint remains a challenging problem due to their sparse nature and lack of explicit connectivity. Traditional methods, such…
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for example, to approximate a point cloud by a low-dimensional…
Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…
This paper introduces Attentive Implicit Representation Networks (AIR-Nets), a simple, but highly effective architecture for 3D reconstruction from point clouds. Since representing 3D shapes in a local and modular fashion increases…
Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a…
Over the years, scene understanding has attracted a growing interest in computer vision, providing the semantic and physical scene information necessary for robots to complete some particular tasks autonomously. In 3D scenes, rich spatial…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in…
Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…
The correlation matrix of massive biomedical data (e.g. gene expression or neuroimaging data) often exhibits a complex and organized, yet latent graph topological structure. We propose a two step procedure that first detects the latent…
Semantic scene understanding from point clouds is particularly challenging as the points reflect only a sparse set of the underlying 3D geometry. Previous works often convert point cloud into regular grids (e.g. voxels or bird-eye view…
Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…
The incorporation of 3D data in facial analysis tasks has gained popularity in recent years. Though it provides a more accurate and detailed representation of the human face, accruing 3D face data is more complex and expensive than 2D face…
Point cloud prediction is an important yet challenging task in the field of autonomous driving. The goal is to predict future point cloud sequences that maintain object structures while accurately representing their temporal motion. These…
Networks offer a powerful approach to modeling complex systems by representing the underlying set of pairwise interactions. Link prediction is the task that predicts links of a network that are not directly visible, with profound…