Related papers: Topological Stability: a New Algorithm for Selecti…

We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to…

Active area of research in AI is the theory of manifold learning and finding lower-dimensional manifold representation on how we can learn geometry from data for providing better quality curated datasets. There are however various issues…

Standard deep learning models for image segmentation cannot guarantee topology accuracy, failing to preserve the correct number of connected components or structures. This, in turn, affects the quality of the segmentations and compromises…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

This paper proposes a novel algorithm for vehicle speed-aided monocular visual-inertial localization using a topological map. The proposed system aims to address the limitations of existing methods that rely heavily on expensive sensors…

To perform visual data exploration, many dimensionality reduction methods have been developed. These tools allow data analysts to represent multidimensional data in a 2D or 3D space, while preserving as much relevant information as…

In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…

Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…

The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…

Estimating the intrinsic dimensionality (ID) of data is a fundamental problem in machine learning and computer vision, providing insight into the true degrees of freedom underlying high-dimensional observations. Existing methods often rely…

It is a critical issue to compute the shortest paths between nodes in networks. Exact algorithms for shortest paths are usually inapplicable for large scale networks due to the high computational complexity. In this paper, we propose a…

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…

We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…

Many distributed learning techniques have been motivated by the increasing size of datasets and their inability to fit into main memory on a single machine. We propose an algorithm that finds the nearest neighbor in a graph locally without…

A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…