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Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented.…
A data structure is presented that explicitly maintains the graph of a Voronoi diagram of $N$ point sites in the plane or the dual graph of a convex hull of points in three dimensions while allowing insertions of new sites/points. Our…
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
Temporal graphs model relationships among entities over time. Recent studies applied temporal graphs to abstract complex systems such as continuous communication among participants of social networks. Often, the amount of data is larger…
Knowledge graphs (KGs) have been increasingly employed for link prediction and recommendation using real-world datasets. However, the majority of current methods rely on static data, neglecting the dynamic nature and the hidden…
Topological Data Analysis (TDA) combines computational topology and data science to extract and analyze intrinsic topological and geometric structures in data set in a metric space. While the persistent homology (PH), a widely used tool in…
Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…
Very large volumes of spatial data increasingly become available and demand effective management. While there has been decades of research on spatial data management, few works consider the current state of commodity hardware, having…
The increasing ability to collect data from urban environments, coupled with a push towards openness by governments, has resulted in the availability of numerous spatio-temporal data sets covering diverse aspects of a city. Discovering…
We investigate a challenging task of dynamic scene geometry estimation, which requires representing both spatial and temporal features. Typically, existing methods align the two features into a unified latent space to model scene geometry.…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
Analytic window query is a commonly used query in the relational databases. It answers the aggregations of data over a sliding window. For example, to get the average prices of a stock for each day. However, it is not supported in the…
In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz, spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate…
In this paper we show that, in the definition of Alexandrov spaces with lower or upper curvature bound, the original conditions can be replaced with much weaker ones. For the purpose, we introduce `imaginary' comparison angles (and…
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…