Related papers: PERCEPT: a new online change-point detection metho…
Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric…
Persistence diagrams (PDs) provide a powerful tool for understanding the topology of the underlying shape of a point cloud. However, identifying which points in PDs encode genuine signals remains challenging. This challenge directly hinders…
Detecting changes in data streams is a vital task in many applications. There is increasing interest in changepoint detection in the online setting, to enable real-time monitoring and support prompt responses and informed decision-making.…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques…
Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the…
Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of…
Graph-based change point detection (CPD) play an irreplaceable role in discovering anomalous graphs in the time-varying network. While several techniques have been proposed to detect change points by identifying whether there is a…
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…
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
One of the main challenges of Topological Data Analysis (TDA) is to extract features from persistent diagrams directly usable by machine learning algorithms. Indeed, persistence diagrams are intrinsically (multi-)sets of points in…
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…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
The aim of online change-point detection is for a accurate, timely discovery of structural breaks. As data dimension outgrows the number of data in observation, online detection becomes challenging. Existing methods typically test only the…
High-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence…
Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving…
Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and…
Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…
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…
A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, the true connections consist of events arriving as streams, which are then aggregated to form edges, ignoring…