Related papers: Online High-Dimensional Change-Point Detection usi…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The…
The extensive emergence of big data techniques has led to an increasing interest in the development of change-point detection algorithms that can perform well in a multivariate, possibly high-dimensional setting. In the current paper, we…
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud…
Standard online change point detection (CPD) methods tend to have large false discovery rates as their detections are sensitive to outliers. To overcome this drawback, we propose Greedy Online Change Point Detection (GOCPD), a…
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…
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…
Building change detection is essential for monitoring urbanization, disaster assessment, urban planning and frequently updating the maps. 3D structure information from airborne light detection and ranging (LiDAR) is very effective for…
Change point analysis is concerned with detecting and locating structure breaks in the underlying model of a sequence of observations ordered by time, space or other variables. A widely adopted approach for change point analysis is to…
Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be…
We study offline change point localization and inference in dynamic multilayer random dot product graphs (D-MRDPGs), where at each time point, a multilayer network is observed with shared node latent positions and time-varying,…
Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…
Change-point analysis is thriving in this big data era to address problems arising in many fields where massive data sequences are collected to study complicated phenomena over time. It plays an important role in processing these data by…
Change point detection is a crucial aspect of analyzing time series data, as the presence of a change point indicates an abrupt and significant change in the process generating the data. While many algorithms for the problem of change point…
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…
In this paper, we study the offline change point localization problem in a sequence of dependent nonparametric random dot product graphs. To be specific, assume that at every time point, a network is generated from a nonparametric random…
The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in…
This paper concerns a theoretical approach that combines topological data analysis (TDA) and sheaf theory. Topological data analysis, a rising field in mathematics and computer science, concerns the shape of the data and has been proven…