Related papers: Online High-Dimensional Change-Point Detection usi…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
Initial development and subsequent calibration of discrete event simulation models for complex systems require accurate identification of dynamically changing process characteristics. Existing data driven change point methods (DD-CPD)…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
How can we detect traffic disturbances from international flight transportation logs or changes to collaboration dynamics in academic networks? These problems can be formulated as detecting anomalous change points in a dynamic graph.…
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of…
Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
Change-point detection (CPD) involves identifying distributional changes in a sequence of independent observations. Among nonparametric methods, rank-based methods are attractive due to their robustness and effectiveness and have been…
Large time-varying graphs are increasingly common in financial, social and biological settings. Feature extraction that efficiently encodes the complex structure of sparse, multi-layered, dynamic graphs presents computational and…
Change-point detection (CPD), which detects abrupt changes in the data distribution, is recognized as one of the most significant tasks in time series analysis. Despite the extensive literature on offline CPD, unsupervised online CPD still…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…
Existing online change-point detection (CPD) methods rely on fixed-dimensional Euclidean summaries, implicitly assuming that distributional changes are well captured by moment-based or feature-based representations. They can obscure…
This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the…
Change Point Detection (CPD) is a critical task in time series analysis, aiming to identify moments when the underlying data-generating process shifts. Traditional CPD methods often rely on unsupervised techniques, which lack adaptability…
Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…
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…
Online change-point detection (OCPD) is important for application in various areas such as finance, biology, and the Internet of Things (IoT). However, OCPD faces major challenges due to high-dimensionality, and it is still rarely studied…
This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…