Optimal Transport Based Change Point Detection and Time Series Segment Clustering

Zou

et al. 2021

Preprint

Online detection of changes in stochastic systems, referred to as sequential change detection or quickest change detection, is an important research topic in statistics, signal processing, and information theory, and has a wide range of applications. This survey starts with the basics of sequential change detection, and then moves on to generalizations and extensions of sequential change detection theory and methods. We also discuss some new dimensions that emerge at the intersection of sequential change detection with other areas, along with a selection of modern applications and remarks on open questions.

Section: B Distribution-free Methodsmentioning

confidence: 99%

Sequential (Quickest) Change Detection: Classical Results and New Directions

Zou

et al. 2021

Preprint

IEEE Open J. Signal Process.

“…The last class is tests based on distance metrics between empirical probability distributions. Prominent among them is the family of integral probability metrics [28] which includes the Maximum Mean Discrepancy (MMD) [29], and the Wasserstein distance [30], which is closely related to the Q-Q based Wasserstein Quantile Test (WQT) [31], [32].…”

Section: Related Workmentioning

confidence: 99%

On Matched Filtering for Statistical Change Point Detection

Cheng

Miller

Hughes

et al. 2020

Self Cite

Non-parametric and distribution-free two-sample tests have been the foundation of many change point detection algorithms. However, randomness in the test statistic as a function of time makes them susceptible to false positives and localization ambiguity. We address these issues by deriving and applying filters matched to the expected temporal signatures of a change for various sliding window, two-sample tests under IID assumptions on the data. These filters are derived asymptotically with respect to the window size for the Wasserstein quantile test, the Wasserstein-1 distance test, Maximum Mean Discrepancy squared (MMD 2 ), and the Kolmogorov-Smirnov (KS) test. The matched filters are shown to have two important properties. First, they are distribution-free, and thus can be applied without prior knowledge of the underlying data distributions. Second, they are peak-preserving, which allows the filtered signal produced by our methods to maintain expected statistical significance. Through experiments on synthetic data as well as activity recognition benchmarks, we demonstrate the utility of this approach for mitigating false positives and improving the test precision. Our method allows for the localization of change points without the use of ad-hoc post-processing to remove redundant detections common to current methods. We further highlight the performance of statistical tests based on the Quantile-Quantile (Q-Q) function and show how the invariance property of the Q-Q function to order-preserving transformations allows these tests to detect change points of different scales with a single threshold within the same dataset.

“…The six activities carried out are staying still, walking, jogging, skipping, taking the stairs up or down. Following respectively [27] and [21], we use the data from person 671 and convert the data to a 1D time series by taking the l 2 -norm of the three-dimensional samples. Human activity recognition data is commonly used in CPD literature [19]- [21], [27], [30], [34], [44].…”

Section: B Data Setsmentioning

confidence: 99%

“…As their method might also delete correct detections, it is clearly not optimal. Recently, the use of a matched filter was investigated as a way to improve detection and localization of change points [27], [30]. It is however difficult to automatically select a representative peak to base the matched filter on [27], nor is it possible to unambiguously derive an asymptotically matched filter [30] for our dissimilarity measure.…”

Section: Postprocessing and Peak Detectionmentioning

confidence: 99%

“…Second, the correlated nature of time series samples is not adequately leveraged by vanilla autoencoders, which makes it challenging to detect abrupt changes in the frequency domain. This is not uncommon in CPD literature [4], [17], [19], [27]. Some methods explicitly focus on abrupt changes in the spectrum [28], [29], thereby often ignoring changes in the time domain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Change Point Detection in Time Series Data using Autoencoders with a Time-Invariant Representation

De Ryck,

De Vos,

Bertrand

2020

Preprint

Change point detection (CPD) aims to locate abrupt property changes in time series data. Recent CPD methods demonstrated the potential of using deep learning techniques, but often lack the ability to identify more subtle changes in the autocorrelation statistics of the signal and suffer from a high false alarm rate. To address these issues, we employ an autoencoderbased methodology with a novel loss function, through which the used autoencoders learn a partially time-invariant representation that is tailored for CPD. The result is a flexible method that allows the user to indicate whether change points should be sought in the time domain, frequency domain or both. Detectable change points include abrupt changes in the slope, mean, variance, autocorrelation function and frequency spectrum. We demonstrate that our proposed method is consistently highly competitive or superior to baseline methods on diverse simulated and real-life benchmark data sets. Finally, we mitigate the issue of false detection alarms through the use of a postprocessing procedure that combines a matched filter and a newly proposed change point score. We show that this combination drastically improves the performance of our method as well as all baseline methods.