Anomalous Points Research Articles

DeepAnT: A Deep Learning Approach for Unsupervised Anomaly Detection in Time Series

Traditional distance and density-based anomaly detection techniques are unable to detect periodic and seasonality related point anomalies which occur commonly in streaming data, leaving a big gap in time series anomaly detection in the current era of the IoT. To address this problem, we present a novel deep learning-based anomaly detection approach (DeepAnT) for time series data, which is equally applicable to the non-streaming cases. DeepAnT is capable of detecting a wide range of anomalies, i.e., point anomalies, contextual anomalies, and discords in time series data. In contrast to the anomaly detection methods where anomalies are learned, DeepAnT uses unlabeled data to capture and learn the data distribution that is used to forecast the normal behavior of a time series. DeepAnT consists of two modules: time series predictor and anomaly detector. The time series predictor module uses deep convolutional neural network (CNN) to predict the next time stamp on the defined horizon. This module takes a window of time series (used as a context) and attempts to predict the next time stamp. The predicted value is then passed to the anomaly detector module, which is responsible for tagging the corresponding time stamp as normal or abnormal. DeepAnT can be trained even without removing the anomalies from the given data set. Generally, in deep learning-based approaches, a lot of data are required to train a model. Whereas in DeepAnT, a model can be trained on relatively small data set while achieving good generalization capabilities due to the effective parameter sharing of the CNN. As the anomaly detection in DeepAnT is unsupervised, it does not rely on anomaly labels at the time of model generation. Therefore, this approach can be directly applied to real-life scenarios where it is practically impossible to label a big stream of data coming from heterogeneous sensors comprising of both normal as well as anomalous points. We have performed a detailed evaluation of 15 algorithms on 10 anomaly detection benchmarks, which contain a total of 433 real and synthetic time series. Experiments show that DeepAnT outperforms the state-of-the-art anomaly detection methods in most of the cases, while performing on par with others.

On the fine structure of the free boundary for the classical obstacle problem

In the classical obstacle problem, the free boundary can be decomposed into “regular” and “singular” points. As shown by Caffarelli in his seminal papers (Caffarelli in Acta Math 139:155–184, 1977; J Fourier Anal Appl 4:383–402, 1998), regular points consist of smooth hypersurfaces, while singular points are contained in a stratified union of $$C^1$$ manifolds of varying dimension. In two dimensions, this $$C^1$$ result has been improved to $$C^{1,\alpha }$$ by Weiss (Invent Math 138:23–50, 1999). In this paper we prove that, for $$n=2$$ singular points are locally contained in a $$C^2$$ curve. In higher dimension $$n\ge 3$$ , we show that the same result holds with $$C^{1,1}$$ manifolds (or with countably many $$C^2$$ manifolds), up to the presence of some “anomalous” points of higher codimension. In addition, we prove that the higher dimensional stratum is always contained in a $$C^{1,\alpha }$$ manifold, thus extending to every dimension the result in Weiss (1999). We note that, in terms of density decay estimates for the contact set, our result is optimal. In addition, for $$n\ge 3$$ we construct examples of very symmetric solutions exhibiting linear spaces of anomalous points, proving that our bound on their Hausdorff dimension is sharp.

Anomalous zero-group-velocity photonic bonding states with local chirality

Photonic crystal waveguides (PCWs) are promising candidates for the basic building blocks of quantum information processing because they support circular polarization points that can unbalance the directionality of an integrated quantum emitter (QE). Nevertheless, the Purcell effect at circular polarization points saturates near the band edge, the preferred region for quantum electrodynamics. Consequently, chirality and ultra-strong light–matter interaction are difficult to combine. Here, we detract from the vicinity of the band edge, and couple modes with different parities by breaking the mirror symmetry. Using the three-dimensional finite-difference time-domain method, simulated band structures of the implemented photonic bonding states (PBS) display single-mode anomalous zero-group-velocity (ZGV) points far from the band edge. The electric field patterns of these points feature circular polarization points at high field intensity regions where a QE would acquire uni-directional emission behavior. Fabricated devices in silicon (Si) slabs demonstrate the predicted coupling energy between the modes and the signature of single-mode anomalous ZGV points. This method to engineer PBS in PCWs paves the way for outperforming chiral light–matter experiments on-chip.

Error-checking intraoperative arterial line blood pressures.

Electronic medical records now store a wealth of intraoperative hemodynamic data. However, analysis of such data is plagued by artifacts related to the monitoring environment. Here, we present an algorithm for automated identification of artifacts and replacement using interpolation of arterial line blood pressures. After IRB approval, minute-by-minute digital recordings of systolic, diastolic, and mean arterial pressures (MAP) obtained during anesthesia care were analyzed using predetermined metrics to identify values anomalous from adjacent neighbors. Anomalous data points were then replaced with linear interpolation of neighbors. The algorithm was then validated against manual artifact identification in 54 anesthesia records and 41,384 arterial line measurements. To assess the algorithm's effect on data analysis, we calculated the percent of time spent with MAP below 55mmHg and above 100mmHg for both raw and conditioned datasets. Manual review of the dataset identified 1.23% of all pressure readings as artifactual. When compared to manual review, the algorithm identified artifacts with 87.0% sensitivity and 99.4% specificity. The average difference between manual review and algorithm in identifying the start of arterial line monitoring was 0.17, and 2.1min for the end of monitoring. Application of the algorithm decreased the percent of time below 55mmHg from 4.3 to 2.0% (2.1% with manual review) and time above 100mmHg from 8.8 to 7.3% (7.3% manual). This algorithm's performance was comparable to manual review by a human anesthesiologist and reduced the incidence of abnormal MAP values identified using a sample analysis tool.

Hyperspectral anomaly detection based on the bilateral filter

Bilateral filter outputs a weighted average of the neighboring information at a pixel. It can smooth the image and remove anomalous points while preserving edges. Inspired by this idea, this paper proposes a hyperspectral anomaly detection algorithm based on the bilateral filter. A pixel that spectrally differs from the background is regarded as anomalous. If every pixel in a hyperspectral image is represented by its surrounding background pixels, a relatively clean hyperspectral background image without anomalies can be obtained. We improve the weights that are imposed on the neighboring pixels in representation. First, spatial distance weight is selected to make full use of the space-varying information. Second, spectral Euclidean distance weight is used to express the spectral similarity. To reduce the negative impact that is caused by anomalies existing in neighboring background pixels, dual window is utilized to act on above two weights. Finally, anomalous information of hyperspectral image can be derived after making the subtraction between the original hyperspectral image and the derived hyperspectral background image. Extensive experiments on three hyperspectral images demonstrate that the proposed method outperforms other benchmark competitors.

Outliers detect methods for time series data

The outliers are unavoidable anomalous points. It will affect the accuracy of time series data. A method of outlier detection and correction for time series data based on statistics is designed in this paper, which can effectively detect the position of anomalous points and make correction. The numerical experimental resultson hotel room night data show that the accuracy of the compressed dataset is improved by 3.4% to 4.4% compared with the original dataset.

Continuous, semi-automatic monitoring of ground deformation using Sentinel-1 satellites

We present the continuous monitoring of ground deformation at regional scale using ESA (European Space Agency) Sentinel-1constellation of satellites. We discuss this operational monitoring service through the case study of the Tuscany Region (Central Italy), selected due to its peculiar geological setting prone to ground instability phenomena. We set up a systematic processing chain of Sentinel-1 acquisitions to create continuously updated ground deformation data to mark the transition from static satellite analysis, based on the analysis of archive images, to dynamic monitoring of ground displacement. Displacement time series, systematically updated with the most recent available Sentinel-1 acquisition, are analysed to identify anomalous points (i.e., points where a change in the dynamic of motion is occurring). The presence of a cluster of persistent anomalies affecting elements at risk determines a significant level of risk, with the necessity of further analysis. Here, we show that the Sentinel-1 constellation can be used for continuous and systematic tracking of ground deformation phenomena at the regional scale. Our results demonstrate how satellite data, acquired with short revisiting times and promptly processed, can contribute to the detection of changes in ground deformation patterns and can act as a key information layer for risk mitigation.

Detecting Regions of Maximal Divergence for Spatio-Temporal Anomaly Detection.

Automatic detection of anomalies in space- and time-varying measurements is an important tool in several fields, e.g., fraud detection, climate analysis, or healthcare monitoring. We present an algorithm for detecting anomalous regions in multivariate spatio-temporal time-series, which allows for spotting the interesting parts in large amounts of data, including video and text data. In opposition to existing techniques for detecting isolated anomalous data points, we propose the "Maximally Divergent Intervals" (MDI) framework for unsupervised detection of coherent spatial regions and time intervals characterized by a high Kullback-Leibler divergence compared with all other data given. In this regard, we define an unbiased Kullback-Leibler divergence that allows for ranking regions of different size and show how to enable the algorithm to run on large-scale data sets in reasonable time using an interval proposal technique. Experiments on both synthetic and real data from various domains, such as climate analysis, video surveillance, and text forensics, demonstrate that our method is widely applicable and a valuable tool for finding interesting events in different types of data.

A BasisEvolution framework for network traffic anomaly detection

Traffic anomalies arise from network problems, and so detection and diagnosis are useful tools for network managers. A great deal of progress has been made on this problem so far, but most approaches can be thought of as forcing the data to fit a single mould. Existing anomaly detection methods largely work by separating traffic signals into “normal” and “anomalous” types using historical data, but do so inflexibly, either requiring a long description for “normal” traffic, or a short, but inaccurate description. In essence, preconceived “basis” functions limit the ability to fit data, and the static nature of many algorithms prevents true adaptivity despite the fact that real Internet traffic evolves over time. In our approach we allow a very general class of functions to represent traffic data, limiting them only by invariant properties of network traffic such as diurnal and weekly cycles. This representation is designed to evolve so as to adapt to changing traffic over time. Our anomaly detection uses thresholding approximation residual error, combined with a generic clustering technique to report a group of anomalous points as a single anomaly event. We evaluate our method with orthogonal matching pursuit, principal component analysis, robust principal component analysis and back propagation neural network, using both synthetic and real world data, and obtaining very low false-alarm probabilities in comparison.

The geometry of nodal sets and outlier detection

Let (M,g) be a compact manifold and let −Δϕk=λkϕk be the sequence of Laplacian eigenfunctions. We present a curious new phenomenon which, so far, we only managed to understand in a few highly specialized cases: the family of functions fN:M→R≥0fN(x)=∑k≤N1λk|ϕk(x)|‖ϕk‖L∞(M) and their extrema seem strangely suited for the detection of anomalous points on the manifold. It may be heuristically interpreted as the sum over distances to the nearest nodal line and potentially hints at a new phenomenon in spectral geometry. We give rigorous statements on the unit square [0,1]2 (where minima localize in Q2) and on Paley graphs (where fN recovers the geometry of quadratic residues of the underlying finite field Fp). Numerical examples show that the phenomenon seems to arise on fairly generic manifolds.

Data Improving in Time Series Using ARX and ANN Models

Anomalous data can negatively impact energy forecasting by causing model parameters to be incorrectly estimated. This paper presents two approaches for the detection and imputation of anomalies in time series data. Autoregressive with exogenous inputs (ARX) and artificial neural network (ANN) models are used to extract the characteristics of time series. Anomalies are detected by performing hypothesis testing on the extrema of the residuals, and the anomalous data points are imputed using the ARX and ANN models. Because the anomalies affect the model coefficients, the data cleaning process is performed iteratively. The models are re-learned on “cleaner” data after an anomaly is imputed. The anomalous data are reimputed to each iteration using the updated ARX and ANN models. The ARX and ANN data cleaning models are evaluated on natural gas time series data. This paper demonstrates that the proposed approaches are able to identify and impute anomalous data points. Forecasting models learned on the unclean data and the cleaned data are tested on an uncleaned out-of-sample dataset. The forecasting model learned on the cleaned data outperforms the model learned on the unclean data with 1.67% improvement in the mean absolute percentage errors and a 32.8% improvement in the root mean squared error. Existing challenges include correctly identifying specific types of anomalies such as negative flows.

On the explicit Torsion Anomalous Conjecture

The Torsion Anomalous Conjecture states that an irreducible variety V V embedded in a semi-abelian variety contains only finitely many maximal V V -torsion anomalous varieties. In this paper we consider an irreducible variety embedded in a product of elliptic curves. Our main result provides a totally explicit bound for the Néron-Tate height of all maximal V V -torsion anomalous points of relative codimension one in the non-CM case, and an analogous effective result in the CM case. As an application, we obtain the finiteness of such points. In addition, we deduce some new explicit results in the context of the effective Mordell-Lang Conjecture; in particular we bound the Néron-Tate height of the rational points of an explicit family of curves of increasing genus.

Application of Drainage Basin Morphotectonic Analysis for Assessment of Tectonic Activities over Two Regional Structures of the Northeast India

ABSTRACT The analysis of drainage basin morphotectonic indices is applied in assessment of the influence of tectonic activity on thirteen selected drainage basins of the streams having linear courses and flowing over two very prominent regional structures of northeast India, viz. the Belt of Schuppen and the Dauki fault. Such analysis has been made in order to assess the influence of tectonic activity of these structures on the morphology of the drainage basins of those streams. The different morphotectonic indices considered are: Basin elongation ratio, hypsometric integral, steepness index and profile concavity, drainage basin asymmetry, valley floor width to valley height ratio, longitudinal profiles, stream length gradient index and mountain front sinuosity. Results of the analysis of the morphotectonic indices of the drainage basins infer that morphology of both the streams and drainage basins have been influenced by the regional structures and the present tectonic status of these two structures varies from active to slightly active phase. No significant influence of lithology is seen in the distribution pattern of the anomalous knick points along the longitudinal profiles. The study also reveals that presently the state of tectonic activity is not uniform within the same regional structure and the Belt of Schuppen is relatively more active as compared to the Dauki fault.

A novel understanding of land use characteristics caused by mining activities: A case study of Wu’an, China

An idea that which zones are the main disturbed areas in mining cities and what are the exact impacts in space concerns re-use and optimal allocation of land. Current research mostly concludes that mining activities impact land use greatly, but there is no definite spatial range of disturbance. To find out the exact range, this paper sets up 12 gradients composed of mineral locations and 11 surrounding gradients with an interval of 3km. And the “D-C-S” (Disturbance-Continuity- Sustainability) framework was then established to evaluate land use characteristics, including 9 indices in the three layers of disturbance, continuity and sustainability. Here, this paper adopted two approaches − transverse land use profiles and anomalous economic points − to test out the understanding of land use characteristics in mining cities. Our findings show that the areas surrounding mineral locations possibly play a more important role in land use structure and functions, designated to 0–9km, especially 3–6km away from mineral locations, where land needs more concerns about optimal allocation for future policy-making to improve the pattern, function and continuity.

A high breakdown, high efficiency and bounded influence modified GM estimator based on support vector regression

ABSTRACTRegression analysis aims to estimate the approximate relationship between the response variable and the explanatory variables. This can be done using classical methods such as ordinary least squares. Unfortunately, these methods are very sensitive to anomalous points, often called outliers, in the data set. The main contribution of this article is to propose a new version of the Generalized M-estimator that provides good resistance against vertical outliers and bad leverage points. The advantage of this method over the existing methods is that it does not minimize the weight of the good leverage points, and this increases the efficiency of this estimator. To achieve this goal, the fixed parameters support vector regression technique is used to identify and minimize the weight of outliers and bad leverage points. The effectiveness of the proposed estimator is investigated using real and simulated data sets.

Respiratory Artefact Removal in Forced Oscillation Measurements: A Machine Learning Approach

Respiratory artefact removal for the forced oscillation technique can be treated as an anomaly detection problem. Manual removal is currently considered the gold standard, but this approach is laborious and subjective. Most existing automated techniques used simple statistics and/or rejected anomalous data points. Unfortunately, simple statistics are insensitive to numerous artefacts, leading to low reproducibility of results. Furthermore, rejecting anomalous data points causes an imbalance between the inspiratory and expiratory contributions. From a machine learning perspective, such methods are unsupervised and can be considered simple feature extraction. We hypothesize that supervised techniques can be used to find improved features that are more discriminative and more highly correlated with the desired output. Features thus found are then used for anomaly detection by applying quartile thresholding, which rejects complete breaths if one of its features is out of range. The thresholds are determined by both saliency and performance metrics rather than qualitative assumptions as in previous works. Feature ranking indicates that our new landmark features are among the highest scoring candidates regardless of age across saliency criteria. F1-scores, receiver operating characteristic, and variability of the mean resistance metrics show that the proposed scheme outperforms previous simple feature extraction approaches. Our subject-independent detector, 1IQR-SU, demonstrated approval rates of 80.6% for adults and 98% for children, higher than existing methods. Our new features are more relevant. Our removal is objective and comparable to the manual method. This is a critical work to automate forced oscillation technique quality control.

RH: An improved AMH aggregate query method

AbstractAs data stream grows exponentially, the aggregate query technique is widely used since it can rapidly obtain the summary information. Typical approximate aggregate query methods, like sliding-window, random sampling, wavelet, sketch index structure, histogram, etc., all evaluate the quality of the algorithms by the average size of query errors and ignore the maximum relative error, which determines the availability of the methods. Regarding this issue, this paper proposes the Reasonable Histogram (RH) method to improve the classic aggregate query method AMH. Based on the analysis of AMH errors’ mathematical characteristics, we build an aggregate query mathematical model based on the Kalman filter, using the optimal estimate of the buckets’ average frequency to calculate the aggregate values of the anomalous points, so as to restrain the maximum relative error.

A Comprehensive Survey on Online Anomaly Detection

Anomaly is a data point that does not follow to the normal points describing the data. Anomaly detection has vital applications in data cleaning and moreover in the mining of anomalous points for fraud recognition, intrusion detection, stock market analysis, customized marketing, system sensors, and email spam detection. Discovering anomalous points among the data points is the fundamental thought to find out an anomaly. Anomaly detection signals out the objects mostly deviating from a particular data set. The majorities of the anomaly detection techniques are normally implemented in batch mode, and so cannot be essentially reached out to largescale problems without giving up the reckoning and memory requirements. To address this problem, existing online anomaly detection technique with oversampling and Principal Component Analysis (PCA), aim at identifying presence of anomalies from a big amount of data via an online updating technique. The oversampling strategy is used to duplicate the target instance and balance the data set and the PCA is used as a renowned unsupervised dimension reduction method, which determines the principal directions of the data distributions. Inspite of the duplication, the computation and memory requirement is reduced using an online updation technique. Thus present framework is ideal for online applications which have reckoning or memory restrictions.

Triangle singularities and XYZ quarkonium peaks

We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. We show that this effect only occurs if masses of resonances in the crossed channel are in a specific, narrow range. We estimate the size of threshold enhancements originating from these anomalous singularities in reactions where the Zc(3900) and the Zb(10610) peaks have been observed.

An Aberrant Pronator Quadratus with Possible Flexor Function at the Wrist

Hand specialists rely on anatomical knowledge to properly assess and treat patients. Our study sought to describe clinically relevant variations that may facilitate accurate diagnoses and effective treatment and management of hand disorders. Forearms from 21 embalmed cadavers (n=42, ages 55‐97, mean 80) were dissected and observed for anomalous attachment points, innervations, muscle shape, and fascicle orientation. Here we report a bilateral aberrant pronator quadratus (PQ) in a single cadaver, whose features suggest its role as a wrist flexor. Typically, the PQ, a flat quadrilateral muscle spanning the distal quarter of the forearm, initiates pronation. Its superficial fibers traverse the anterior surfaces of the radius and ulna, while its deep fibers bind them together. The aberrant PQ has both superficial and deep bellies originating on the lateral surfaces of these bones with the muscle fascicles oriented obliquely (pennation=80° for radial bellies, bilaterally; 60° for left, 48° for right ulnar bellies). Each PQ has tendons from the radial (1 from right, 2 from left) and ulnar bellies (2 from right, 1 from left). In both forearms, these form a common tendon that travels distally across the radioulnar joint, through the carpal tunnel floor, and inserts onto the capitate. Collectively, these features suggest an additional function of wrist flexion, similar to a rare flexor carpi radialis brevis. Thus, the aberrant PQ may not have been the typical initiator of forearm pronation, and perhaps other muscles compensated, i.e., pronator teres, brachioradialis, and/or flexor carpi radialis. To conclude, awareness of diverse hand anatomy is critical for clinical examination and management of hand disorders.