Related papers: Topological Data Analysis (TDA) for Time Series
Topological Data Analysis (TDA) gives practioners the ability to analyse the global structure of cybersecurity data. We use TDA for anomaly detection in host-based logs collected with the open-source Logging Made Easy (LME) project. We…
Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically…
In this work the significance of treating a set of measurements as a time series is being explored. Time Series Analysis (TSA) techniques, part of the Exploratory Data Analysis (EDA) approach, can provide much insight regarding the…
In many real-world application, e.g., speech recognition or sleep stage classification, data are captured over the course of time, constituting a Time-Series. Time-Series often contain temporal dependencies that cause two otherwise…
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the network and summarize…
Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…
This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of…
With the recent advances in technology, a wide range of systems continue to collect a large amount of data over time and thus generate time series. Time-Series Anomaly Detection (TSAD) is an important task in various time-series…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features…
We introduce a method of time series analysis for two-dimensional transient flow patterns based on Topological Flow Data Analysis (TFDA), a new approach to topological data analysis. TFDA identifies local topological flow structures from an…
The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
Time series anomaly detection is a challenging problem due to the complex temporal dependencies and the limited label data. Although some algorithms including both traditional and deep models have been proposed, most of them mainly focus on…
Time series anomaly detection has applications in a wide range of research fields and applications, including manufacturing and healthcare. The presence of anomalies can indicate novel or unexpected events, such as production faults, system…
Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…
In recent decades, hypergraphs and their analysis through Topological Data Analysis (TDA) have emerged as powerful tools for understanding complex data structures. Various methods have been developed to construct hypergraphs -- referred to…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…