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Time series segmentation, which is also known as multiple‐change‐point detection, is a well‐established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second‐order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms and cross‐periodograms of the components of the input time series. However, the standard ‘maximum’ and ‘average’ methods for doing so often fail in high dimensions when, for example, the change points are sparse across the panel or the cumulative sum statistics are spuriously large. We propose the sparsified binary segmentation algorithm which aggregates the cumulative sum statistics by adding only those that pass a certain threshold. This ‘sparsifying’ step reduces the influence of irrelevant noisy contributions, which is particularly beneficial in high dimensions. To show the consistency of sparsified binary segmentation, we introduce the multivariate locally stationary wavelet model for time series, which is a separate contribution of this work.

Background Ovarian cancer is the most lethal of all gynecological cancers. Cancer Antigen 125 (CA125) is the best‐performing ovarian cancer biomarker which however is still not effective as a screening test in the general population. Recent literature reports additional biomarkers with the potential to improve on CA125 for early detection when using longitudinal multimarker models. Methods Our data comprised 180 controls and 44 cases with serum samples sourced from the multimodal arm of UK Collaborative Trial of Ovarian Cancer Screening (UKCTOCS). Our models were based on Bayesian change‐point detection and recurrent neural networks. Results We obtained a significantly higher performance for CA125–HE4 model using both methodologies (AUC 0.971, sensitivity 96.7% and AUC 0.987, sensitivity 96.7%) with respect to CA125 (AUC 0.949, sensitivity 90.8% and AUC 0.953, sensitivity 92.1%) for Bayesian change‐point model (BCP) and recurrent neural networks (RNN) approaches, respectively. One year before diagnosis, the CA125–HE4 model also ranked as the best, whereas at 2 years before diagnosis no multimarker model outperformed CA125. Conclusions Our study identified and tested different combination of biomarkers using longitudinal multivariable models that outperformed CA125 alone. We showed the potential of multivariable models and candidate biomarkers to increase the detection rate of ovarian cancer. Using the data from largest prospective ovarian cancer clinical trial, we assessed, for the first time, the performance of deep and statistical learning approaches in evaluating of the panel longitudinal biomarkers. Our results demonstrate that these models outperform CA125, the single best ovarian cancer biomarker. These findings underscore the potential of multimarker models in improving the detection rate of ovarian cancer and have significant implications for the field of cancer screening and early detection.

Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t)=μ(t)+Σ1[less-than or equal to]l<[infinity]ηi, l+ vl(t), where μ is the common mean, vl are the eigenfunctions of the covariance operator and the ηi, l are the scores. Inferential procedures assume that the mean function μ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s), the results of principal component analysis are confounded by the change(s). It is therefore important to develop a methodology to test the assumption of a common functional mean. We develop such a test using quantities which can be readily computed in the R package fda. The null distribution of the test statistic is asymptotically pivotal with a well-known asymptotic distribution. The asymptotic test has excellent finite sample performance. Its application is illustrated on temperature data from England.

Due to the diversity of ship-radiated noise (SRN), audio segmentation is an essential procedure in the ship statuses/categories identification. However, the existing segmentation methods are not suitable for the SRN because of the lack of prior knowledge. In this paper, by a generalized likelihood ratio (GLR) test on the ordinal pattern distribution (OPD), we proposed a segmentation criterion and introduce it into single change-point detection (SCPD) and multiple change-points detection (MCPD) for SRN. The proposed method is free from the acoustic feature extraction and the corresponding probability distribution estimation. In addition, according to the sequential structure of ordinal patterns, the OPD is efficiently estimated on a series of analysis windows. By comparison with the Bayesian Information Criterion (BIC) based segmentation method, we evaluate the performance of the proposed method on both synthetic signals and real-world SRN. The segmentation results on synthetic signals show that the proposed method estimates the number and location of the change-points more accurately. The classification results on real-world SRN show that our method obtains more distinguishable segments, which verifies its effectiveness in SRN segmentation.

A two-stage procedure for simultaneously detecting multiple change-points in linear models is developed. In the cutting stage, the change-point problem is converted into a model selection problem so that a modern model selection method can be applied. In the refining stage, the change-points obtained in the cutting stage are finalized via a refining method. Under mild conditions, consistency of the number of change-point estimates is established. The new procedure is fast and accurate, as shown in simulation studies. Its applicability in real situations is demonstrated via well-log and ozone data. Les auteurs développent une procédure en deux étapes pour la détection simultanée de plusieurs points de rupture dans les modèles linéaires. À l'étape de découpage, le problème de points de rupture est transformé en un problème de sélection de modèle afin d'y appliquer une méthode moderne de sélection. La deuxième étape consiste ensuite à raffiner les points de rupture obtenus. Les auteurs établissent la convergence de l'estimateur du nombre de points de rupture sous des hypothèses modérées. Ils montrent à l'aide d'études de simulation que la nouvelle procédure est rapide et précise, puis illustrent son usage à l'aide de données réelles portant sur la réponse magnétique à l'intérieur d'un puit, ainsi que sur l'ozone.

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured graph data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we give a general framework for the algorithms categorized under various settings: unsupervised versus (semi-)supervised approaches, for static versus dynamic graphs, for attributed versus plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly attribution and highlight the major techniques that facilitate digging out the root cause, or the ‘why’, of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to a significant increase in computational complexity. WBS is also easy to code. We propose two stopping criteria for WBS: one based on thresholding and the other based on what we term the 'strengthened Schwarz information criterion'. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance in comparison with the state of the art. The WBS methodology is implemented in the R package wbs, available on CRAN. In addition, we provide a new proof of consistency of binary segmentation with improved rates of convergence, as well as a corresponding result for WBS.

Many applications of metal oxide gas sensors can benefit from reliable algorithms to detect significant changes in the sensor response. Significant changes indicate a change in the emission modality of a distant gas source and occur due to a sudden change of concentration or exposure to a different compound. As a consequence of turbulent gas transport and the relatively slow response and recovery times of metal oxide sensors, their response in open sampling configuration exhibits strong fluctuations that interfere with the changes of interest. In this paper we introduce TREFEX, a novel change point detection algorithm, especially designed for metal oxide gas sensors in an open sampling system. TREFEX models the response of MOX sensors as a piecewise exponential signal and considers the junctions between consecutive exponentials as change points. We formulate non-linear trend filtering and change point detection as a parameter-free convex optimization problem for single sensors and sensor arrays. We evaluate the performance of the TREFEX algorithm experimentally for different metal oxide sensors and several gas emission profiles. A comparison with the previously proposed GLR method shows a clearly superior performance of the TREFEX algorithm both in detection performance and in estimating the change time.

Timely detecting disturbances and locating their sources are critical to the reliable operation of power grids. This capability enables operators to effectively diagnose disturbances over wide areas and earns time for remedial reactions. In this study, a travelling‐wave based scheme, namely data‐driven online distributed disturbance location (DODDL), is proposed to quickly detect disturbances and determine their geographic location in large‐scale power grids when the grids’ topology is not available. The proposed DODDL scheme consists of two function blocks: (i) a singular spectrum analysis‐based change‐point detection method, which can quickly detect disturbances and determine their arrival time at distributed sensors, and (ii) a novel temporal scanning algorithm, which can accurately determine the geographic location of the disturbance source point. Utilising field measurement data sets recorded by the frequency disturbance recorders from the frequency monitoring network, it is shown that the DODDL scheme is not only quicker and more robust to grid non‐homogeneity than existing approaches, but also can capture and locate more subtle and concealed disturbances.

Change points are abrupt variations in time series data. Such abrupt changes may represent transitions that occur between states. Detection of change points is useful in modelling and prediction of time series and is found in application areas such as medical condition monitoring, climate change detection, speech and image analysis, and human activity analysis. This survey article enumerates, categorizes, and compares many of the methods that have been proposed to detect change points in time series. The methods examined include both supervised and unsupervised algorithms that have been introduced and evaluated. We introduce several criteria to compare the algorithms. Finally, we present some grand challenges for the community to consider.