Online High-Dimensional Change-Point Detection using Topological Data Analysis

by   Xiaojun Zheng, et al.

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 structures for a wide range of applications, including protein classification, neuroscience, and time-series analysis. However, in many such applications, one is also interested in sequentially detecting changes in this topological structure. We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles this problem by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection. The key novelty in PD-CP is that it leverages the distribution of points on persistence diagrams for online detection of topological changes. We demonstrate the effectiveness of PD-CP in an application to solar flare monitoring.



There are no comments yet.


page 1

page 2

page 3

page 4


Harnessing the power of Topological Data Analysis to detect change points in time series

We introduce a novel geometry-oriented methodology, based on the emergin...

A computationally efficient framework for vector representation of persistence diagrams

In Topological Data Analysis, a common way of quantifying the shape of d...

Change-point detection using spectral PCA for multivariate time series

We propose a two-stage approach Spec PC-CP to identify change points in ...

Selective Inference for Multi-Dimensional Multiple Change Point Detection

We consider the problem of multiple change point (CP) detection from a m...

ATOL: Automatic Topologically-Oriented Learning

There are abundant cases for using Topological Data Analysis (TDA) in a ...

EVARS-GPR: EVent-triggered Augmented Refitting of Gaussian Process Regression for Seasonal Data

Time series forecasting is a growing domain with diverse applications. H...

NEWMA: a new method for scalable model-free online change-point detection

We consider the problem of detecting abrupt changes in the distribution ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.