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Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Network traffic classification is a core primitive for network security and management, yet it is increasingly challenged by pervasive encryption and evolving protocols. A central bottleneck is representation: hand-crafted flow statistics…
Analyzing high-dimensional data and finding hidden patterns is a difficult problem and has attracted numerous research efforts. Automated methods can be useful to some extent but bringing the data analyst into the loop via interactive…
Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…
Topological data analysis aims to extract topological quantities from data, which tend to focus on the broader global structure of the data rather than local information. The Mapper method, specifically, generalizes clustering methods to…
The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and…
Graph layout is the process of creating a visual representation of a graph through a node-link diagram. Node-attribute graphs have additional data stored on the nodes which describe certain properties of the nodes called attributes. Typical…
Critical networking workflows require high-fidelity packet captures (PCAPs) for testing, security analysis, and protocol validation, not just statistical flow-level summaries. Recent packet generators have demonstrated protocol-constrained…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
Topology at the undergraduate level is often a theoretical mathematics course, introducing concepts from point-set topology or possibly algebraic topology. However, the last two decades have seen an explosion of growth in applied topology…
Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
Tag clouds provide an aggregate of tag-usage statistics. They are typically sent as in-line HTML to browsers. However, display mechanisms suited for ordinary text are not ideal for tags, because font sizes may vary widely on a line. As…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
Keypoint-based representation has proven advantageous in various visual and robotic tasks. However, the existing 2D and 3D methods for detecting keypoints mainly rely on geometric consistency to achieve spatial alignment, neglecting…
There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem…
In this paper, we propose a path following replicator dynamic, and investigate its potentials in uncovering the underlying cluster structure of a graph. The proposed dynamic is a generalization of the discrete replicator dynamic. The…
In enterprise datasets, documents are rarely pure. They are not just text, nor just numbers; they are a complex amalgam of narrative and structure. Current Retrieval-Augmented Generation (RAG) systems have attempted to address this…
Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…