Related papers: Integrating Space, Time, Version and Scale Using A…

A state-space model is a statistical framework for inferring latent states from observed time-series data. However, inference with nonlinear and high-dimensional state-space models remains challenging. To this end, an approach based on…

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…

Data warehouse store and provide access to large volume of historical data supporting the strategic decisions of organisations. Data warehouse is based on a multidimensional model which allow to express user's needs for supporting the…

Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to…

Spatial-temporal data collected across different geographic locations often suffer from missing values, posing challenges to data analysis. Existing methods primarily leverage fixed spatial graphs to impute missing values, which implicitly…

We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…

We introduce a spatial graph and hypergraph model that smoothly interpolates between a graph with purely pairwise edges and a graph where all connections are in large hyperedges. The key component is a spatial clustering resolution…

In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. Using this definition we prove: - A bounded-curvature surface embedded spaces TSP admits to a PTAS. -…

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…

We provide a comprehensive overview of current approaches and systems for combining graphs and time series data. We categorize existing systems into four architectural categories and analyze how these systems meet different requirements and…

Tabular data in relational databases represents a significant portion of industrial data. Hence, analyzing and interpreting tabular data is of utmost importance. Application tasks on tabular data are manifold and are often not specified…

This paper represents an approach to creating global knowledge systems, using new philosophy and infrastructure of global distributed semantic network (frame knowledge representation system) based on the space-time database construction.…

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…

The number of mobile devices (e.g., smartphones, wearable technologies) is rapidly growing. In line with this trend, a massive amount of spatial data is being collected since these devices allow users to geo-tag user-generated content.…

Graph machine learning has led to a significant increase in the capabilities of models that learn on arbitrary graph-structured data and has been applied to molecules, social networks, recommendation systems, and transportation, among other…

Pandemics, with their profound societal and economic impacts, pose significant threats to global health, mortality rates, economic stability, and political landscapes. In response to these challenges, numerous studies have employed…

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…