Related papers: A Novel and Efficient Data Point Neighborhood Cons…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…
In historical studies, the older the sources, the more common it is to have access to data that are only partial, and/or unreliable or imprecise. This can make it difficult, or even impossible, to perform certain tasks of interest, such as…
We are interested in the problem of finding $k$ nearest neighbours in the plane and in the presence of polygonal obstacles ($\textit{OkNN}$). Widely used algorithms for OkNN are based on incremental visibility graphs, which means they…
The k-Nearest Neighbor (kNN) classification approach is conceptually simple - yet widely applied since it often performs well in practical applications. However, using a global constant k does not always provide an optimal solution, e.g.,…
In an era of knowledge-based economy, commercialized research and globalized competition for talent, the creation of innovation ecosystems and innovation networks is at the forefront of efforts of cities. In this context, public…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…
Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…
The local arrangement of atoms is one of the most important predictors of mechanical and functional properties of materials. However, algorithms for identifying the geometrical arrangements of atoms in complex materials systems are lacking.…
$\newcommand{\dist}{\operatorname{dist}}$ In this paper we define the notion of a probabilistic neighborhood in spatial data: Let a set $P$ of $n$ points in $\mathbb{R}^d$, a query point $q \in \mathbb{R}^d$, a distance metric $\dist$, and…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
The shape of circle is one of fundamental geometric primitives of man-made engineering objects. Thus, extraction of circles from scanned point clouds is a quite important task in 3D geometry data processing. However, existing circle…
In this paper, we present a deep learning architecture which addresses the problem of 3D semantic segmentation of unstructured point clouds. Compared to previous work, we introduce grouping techniques which define point neighborhoods in the…
One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network.…
Accurate tracking in urban environments necessitates target birth, survival, and detection models that quantify the impact of terrain and building geometry on the sequential estimation procedure. Current efforts assume that target…
Many real world systems or web services can be represented as a network such as social networks and transportation networks. In the past decade, many algorithms have been developed to detect the communities in a network using connections…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Skyline queries are important in many application domains. In this paper, we propose a novel structure Skyline Diagram, which given a set of points, partitions the plane into a set of regions, referred to as skyline polyominos. All query…
Discovering communities in complex networks means grouping nodes similar to each other, to uncover latent information about them. There are hundreds of different algorithms to solve the community detection task, each with its own…
Community detection plays a crucial role in understanding the structural organization of complex networks. Previous methods, particularly those from statistical physics, primarily focus on the analysis of mesoscopic network structures and…