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Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much…

Machine Learning · Computer Science 2024-11-01 Sebastian Damrich , Philipp Berens , Dmitry Kobak

Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…

Algebraic Topology · Mathematics 2019-07-23 Mehmet Emin Aktas , Esra Akbas , Ahmed El Fatmaoui

Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not…

Computational Geometry · Computer Science 2013-10-03 Ulrich Bauer , Michael Kerber , Jan Reininghaus

We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…

Statistics Theory · Mathematics 2025-12-30 Toshiyuki Nakayama

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…

Flow cardinality estimation is the problem of estimating the number of distinct elements in a data flow, often with a stringent memory constraint. It has wide applications in network traffic measurement and in database systems. The virtual…

Information Theory · Computer Science 2018-12-10 Zeyu Zhou

Measuring network flow sizes is important for tasks like accounting/billing, network forensics and security. Per-flow accounting is considered hard because it requires that many counters be updated at a very high speed; however, the large…

Networking and Internet Architecture · Computer Science 2007-10-07 Yi Lu , Andrea Montanari , Balaji Prabhakar

Monitoring tasks, such as anomaly and DDoS detection, require identifying frequent flow aggregates based on common IP prefixes. These are known as \emph{hierarchical heavy hitters} (HHH), where the hierarchy is determined based on the type…

Data Structures and Algorithms · Computer Science 2017-07-24 Ran Ben Basat , Gil Einziger , Roy Friedman , Marcelo Caggiani Luizelli , Erez Waisbard

Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…

Machine Learning · Statistics 2026-01-13 Yueqi Cao , Anthea Monod

Consistent hashing is a technique for distributing data across a network of nodes in a way that minimizes reorganization when nodes join or leave the network. It is extensively applied in modern distributed systems as a fundamental…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-18 Massimo Coluzzi , Amos Brocco , Alessandro Antonucci , Tiziano Leidi

Finding persistent sparse (PS) flow is critical to early warning of many threats. Previous works have predominantly focused on either heavy or persistent flows, with limited attention given to PS flows. Although some recent studies pay…

Data Structures and Algorithms · Computer Science 2025-05-09 Jiayao Wang , Qilong Shi , Xiyan Liang , Han Wang , Wenjun Li , Ziling Wei , Weizhe Zhang , Shuhui Chen

Streamflow is a dynamical process that integrates water movement in space and time within basin boundaries. The authors characterize the dynamics associated with streamflow time series data from about seventy-one U.S. Geological Survey…

Physics and Society · Physics 2021-04-14 Ganesh R. Ghimire , Navid Jadidoleslam , Witold F. Krajewski , Anastasios A. Tsonis

Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…

Algebraic Topology · Mathematics 2023-06-21 Mehmet Emin Aktas , Thu Nguyen , Rakin Riza , Muhammad Ifte Islam , Esra Akbas

Estimating the correspondences between pixels in sequences of images is a critical first step for a myriad of tasks including vision-aided navigation (e.g., visual odometry (VO), visual-inertial odometry (VIO), and visual simultaneous…

Image and Video Processing · Electrical Eng. & Systems 2018-03-16 E. Jared Shamwell , William D. Nothwang , Donald Perlis

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…

Algebraic Topology · Mathematics 2016-12-16 Nicholas A. Scoville , Karthik Yegnesh

Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…

Signal Processing · Electrical Eng. & Systems 2020-05-05 Yu-Min Chung , Chuan-Shen Hu , Yu-Lun Lo , Hau-Tieng Wu

Fast detection of heavy flows (e.g., heavy hitters and heavy changers) in massive network traffic is challenging due to the stringent requirements of fast packet processing and limited resource availability. Invertible sketches are summary…

Networking and Internet Architecture · Computer Science 2020-07-23 Lu Tang , Qun Huang , Patrick P. C. Lee

Collecting flow records is a common practice of network operators and researchers for monitoring, diagnosing and understanding a network. Traditional tools like NetFlow face great challenges when both the speed and the complexity of the…

Networking and Internet Architecture · Computer Science 2018-12-06 Zongyi Zhao , Xingang Shi , Xia Yin , Zhiliang Wang

Network measurement is necessary to obtain an understanding of the network traffic and keep the network healthy. Flow-level measurement is widely used because it provides rich enough information while being resource efficient, in contrast…

Networking and Internet Architecture · Computer Science 2018-12-10 Zongyi Zhao , Xingang Shi , Xia Yin , Zhiliang Wang

We evaluate methods for applying unsupervised anomaly detection to cybersecurity applications on computer network traffic data, or flow. We borrow from the natural language processing literature and conceptualize flow as a sort of…

Cryptography and Security · Computer Science 2018-05-15 Benjamin J. Radford , Bartley D. Richardson , Shawn E. Davis
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