Related papers: Persistence-Based Statistics for Detecting Structu…
What is the "right" topological invariant of a large point cloud X? Prior research has focused on estimating the full persistence diagram of X, a quantity that is very expensive to compute, unstable to outliers, and far from a sufficient…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
We study the parametric online changepoint detection problem, where the underlying distribution of the streaming data changes from a known distribution to an alternative that is of a known parametric form but with unknown parameters. We…
We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet…
In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate…
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…
This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These…
Advanced 3D metrology technologies such as Coordinate Measuring Machine (CMM) and laser 3D scanners have facilitated the collection of massive point cloud data, beneficial for process monitoring, control and optimization. However, due to…
Very long and noisy sequence data arise from biological sciences to social science including high throughput data in genomics and stock prices in econometrics. Often such data are collected in order to identify and understand shifts in…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
This paper studies high-dimensional trend inference for piecewise smooth signals under nonstationary noise and asynchronous structural breaks by first detecting asynchronous changes without assuming stationarity and then further exploiting…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
We propose an alternative formulation of the well-known Hough transform to detect lines in point clouds. Replacing the discretized voting scheme of the classical Hough transform by a continuous score function, its persistent features in the…
We propose the first Bayesian methods for detecting change points in high-dimensional mean and covariance structures. These methods are constructed using pairwise Bayes factors, leveraging modularization to identify significant changes in…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
We consider the challenge of efficiently detecting changes within a network of sensors, where we also need to minimise communication between sensors and the cloud. We propose an online, communication-efficient method to detect such changes.…
This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…