Identification of errors or anomalous values, collectively considered outliers, assists in exploring data or through removing outliers improves statistical analysis. In biomechanics, outlier detection methods have explored the ‘shape’ of the entire cycles, although exploring fewer points using a ‘moving-window’ may be advantageous. Hence, the aim was to develop a moving-window method for detecting trials with outliers in intra-participant time-series data. Outliers were detected through two stages for the strides (mean 38 cycles) from treadmill running. Cycles were removed in stage 1 for one-dimensional (spatial) outliers at each time point using the median absolute deviation, and in stage 2 for two-dimensional (spatial–temporal) outliers using a moving window standard deviation. Significance levels of the t-statistic were used for scaling. Fewer cycles were removed with smaller scaling and smaller window size, requiring more stringent scaling at stage 1 (mean 3.5 cycles removed for 0.0001 scaling) than at stage 2 (mean 2.6 cycles removed for 0.01 scaling with a window size of 1). Settings in the supplied Matlab code should be customised to each data set, and outliers assessed to justify whether to retain or remove those cycles. The method is effective in identifying trials with outliers in intra-participant time series data.

There has been a tremendous increase in the volume of sensor data collected over the last decade for different monitoring tasks. For example, petabytes of earth science data are collected from modern satellites, in-situ sensors and different climate models. Similarly, huge amount of flight operational data is downloaded for different commercial airlines. These different types of datasets need to be analyzed for finding outliers. Information extraction from such rich data sources using advanced data mining methodologies is a challenging task not only due to the massive volume of data, but also because these datasets are physically stored at different geographical locations with only a subset of features available at any location. Moving these petabytes of data to a single location may waste a lot of bandwidth. To solve this problem, in this paper, we present a novel algorithm which can identify outliers in the entire data without moving all the data to a single location. The method we propose only centralizes a very small sample from the different data subsets at different locations. We analytically prove and experimentally verify that the algorithm offers high accuracy compared to complete centralization with only a fraction of the communication cost. We show that our algorithm is highly relevant to both earth sciences and aeronautics by describing applications in these domains. The performance of the algorithm is demonstrated on two large publicly available datasets: (1) the NASA MODIS satellite images and (2) a simulated aviation dataset generated by the ‘Commercial Modular Aero-Propulsion System Simulation’ (CMAPSS).

These files are supplements to the paper titled 'A Robust Two-step Method for Detection of Outlier Sets'.This paper identifies and addresses the need for a robust method that identifies sets of points that collectively deviate from typical patterns in a dataset, which it calls "outlier sets'', while excluding individual points from detection. This new methodology, Outlier Set Two-step Identification (OSTI) employs a two-step approach to detect and label these outlier sets. First, it uses Gaussian Mixture Models for probabilistic clustering, identifying candidate outlier sets based on cluster weights below a predetermined threshold. Second, OSTI measures the Inter-cluster Mahalanobis distance between each candidate outlier set's centroid and the overall dataset mean. OSTI then tests the null hypothesis that this distance does not significantly differ from its theoretical chi-square distribution, enabling the formal detection of outlier sets. We test OSTI systematically on 8,000 synthetic 2D datasets across various inlier configurations and thousands of possible outlier set characteristics. Results show OSTI robustly and consistently detects outlier sets with an average F1 score of 0.92 and an average purity (the degree to which outlier sets identified correspond to those generated synthetically, i.e., our ground truth) of 98.58%. We also compare OSTI with state-of-the-art outlier detection methods, to illuminate how OSTI fills a gap as a tool for the exclusive detection of outlier sets.

ensuring accurate representations in spatial and temporal data analyses.

ABSTRACT The considerable volume of data generated by sensors in the field presents systematic errors; thus, it is extremely important to exclude these errors to ensure mapping quality. The objective of this research was to develop and test a methodology to identify and exclude outliers in high-density spatial data sets, determine whether the developed filter process could help decrease the nugget effect and improve the spatial variability characterization of high sampling data. We created a filter composed of a global, anisotropic, and an anisotropic local analysis of data, which considered the respective neighborhood values. For that purpose, we used the median to classify a given spatial point into the data set as the main statistical parameter and took into account its neighbors within a radius. The filter was tested using raw data sets of corn yield, soil electrical conductivity (ECa), and the sensor vegetation index (SVI) in sugarcane. The results showed an improvement in accuracy of spatial variability within the data sets. The methodology reduced RMSE by 85 %, 97 %, and 79 % in corn yield, soil ECa, and SVI respectively, compared to interpolation errors of raw data sets. The filter excluded the local outliers, which considerably reduced the nugget effects, reducing estimation error of the interpolated data. The methodology proposed in this work had a better performance in removing outlier data when compared to two other methodologies from the literature.

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Anomaly Detection Market Size 2025-2029

The anomaly detection market size is forecast to increase by USD 4.44 billion at a CAGR of 14.4% between 2024 and 2029.

The market is experiencing significant growth, particularly in the BFSI sector, as organizations increasingly prioritize identifying and addressing unusual patterns or deviations from normal business operations. The rising incidence of internal threats and cyber frauds necessitates the implementation of advanced anomaly detection tools to mitigate potential risks and maintain security. However, implementing these solutions comes with challenges, primarily infrastructural requirements. Ensuring compatibility with existing systems, integrating new technologies, and training staff to effectively utilize these tools pose significant hurdles for organizations.
Despite these challenges, the potential benefits of anomaly detection, such as improved risk management, enhanced operational efficiency, and increased security, make it an essential investment for businesses seeking to stay competitive and agile in today's complex and evolving threat landscape. Companies looking to capitalize on this market opportunity must carefully consider these challenges and develop strategies to address them effectively. Cloud computing is a key trend in the market, as cloud-based solutions offer quick deployment, flexibility, and scalability.

What will be the Size of the Anomaly Detection Market during the forecast period?

Explore in-depth regional segment analysis with market size data - historical 2019-2023 and forecasts 2025-2029 - in the full report.
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In the dynamic and evolving market, advanced technologies such as resource allocation, linear regression, pattern recognition, and support vector machines are increasingly being adopted for automated decision making. Businesses are leveraging these techniques to enhance customer experience through behavioral analytics, object detection, and sentiment analysis. Machine learning algorithms, including random forests, naive Bayes, decision trees, clustering algorithms, and k-nearest neighbors, are essential tools for risk management and compliance monitoring. AI-powered analytics, time series forecasting, and predictive modeling are revolutionizing business intelligence, while process optimization is achieved through the application of decision support systems, natural language processing, and predictive analytics.
Computer vision, image recognition, logistic regression, and operational efficiency are key areas where principal component analysis and artificial technoogyneural networks contribute significantly. Speech recognition and operational efficiency are also benefiting from these advanced technologies, enabling businesses to streamline processes and improve overall performance.

How is this Anomaly Detection Industry segmented?

The anomaly detection industry research report provides comprehensive data (region-wise segment analysis), with forecasts and estimates in 'USD million' for the period 2025-2029, as well as historical data from 2019-2023 for the following segments.

Deployment

  Cloud
  On-premises


Component

  Solution
  Services


End-user

  BFSI
  IT and telecom
  Retail and e-commerce
  Manufacturing
  Others


Technology

  Big data analytics
  AI and ML
  Data mining and business intelligence


Geography

  North America

    US
    Canada
    Mexico


  Europe

    France
    Germany
    Spain
    UK


  APAC

    China
    India
    Japan


  Rest of World (ROW)

By Deployment Insights

The cloud segment is estimated to witness significant growth during the forecast period. The market is witnessing significant growth due to the increasing adoption of advanced technologies such as machine learning models, statistical methods, and real-time monitoring. These technologies enable the identification of anomalous behavior in real-time, thereby enhancing network security and data privacy. Anomaly detection algorithms, including unsupervised learning, reinforcement learning, and deep learning networks, are used to identify outliers and intrusions in large datasets. Data security is a major concern, leading to the adoption of data masking, data pseudonymization, data de-identification, and differential privacy.

Data leakage prevention and incident response are critical components of an effective anomaly detection system. False positive and false negative rates are essential metrics to evaluate the performance of these systems. Time series analysis and concept drift are important techniques used in anomaly detection. Data obfuscation, data suppression, and data aggregation are other strategies employed to maintain data privacy. Companies such as Anodot, Cisco Systems Inc, IBM Corp, and SAS Institute Inc offer both cloud-based and on-premises anomaly detection solutions. These soluti

We present a set of novel algorithms which we call sequenceMiner, that detect and characterize anomalies in large sets of high-dimensional symbol sequences that arise from recordings of switch sensors in the cockpits of commercial airliners. While the algorithms we present are general and _domain-independent, we focus on a specific problem that is critical to determining system-wide health of a fleet of aircraft. The approach taken uses unsupervised clustering of sequences using the normalized length of he longest common subsequence (nLCS) as a similarity measure, followed by a detailed analysis of outliers to detect anomalies. In this method, an outlier sequence is defined as a sequence that is far away from a cluster. We present new algorithms for outlier analysis that provide comprehensible indicators as to why a particular sequence is deemed to be an outlier. The algorithm provides a coherent description to an analyst of the anomalies in the sequence when compared to more normal sequences. The final section of the paper demonstrates the effectiveness of sequenceMiner for anomaly detection on a real set of discrete sequence data from a fleet of commercial airliners. We show that sequenceMiner discovers actionable and operationally significant safety events. We also compare our innovations with standard HiddenMarkov Models, and show that our methods are superior

As an important technique for data pre-processing, outlier detection plays a crucial role in various real applications and has gained substantial attention, especially in medical fields. Despite the importance of outlier detection, many existing methods are vulnerable to the distribution of outliers and require prior knowledge, such as the outlier proportion. To address this problem to some extent, this article proposes an adaptive mini-minimum spanning tree-based outlier detection (MMOD) method, which utilizes a novel distance measure by scaling the Euclidean distance. For datasets containing different densities and taking on different shapes, our method can identify outliers without prior knowledge of outlier percentages. The results on both real-world medical data corpora and intuitive synthetic datasets demonstrate the effectiveness of the proposed method compared to state-of-the-art methods.

Understanding the statistics of fluctuation driven flows in the boundary layer of magnetically confined plasmas is desired to accurately model the lifetime of the vacuum vessel components. Mirror Langmuir probes (MLPs) are a novel diagnostic that uniquely allow us to sample the plasma parameters on a time scale shorter than the characteristic time scale of their fluctuations. Sudden large-amplitude fluctuations in the plasma degrade the precision and accuracy of the plasma parameters reported by MLPs for cases in which the probe bias range is of insufficient amplitude. While some data samples can readily be classified as valid and invalid, we find that such a classification may be ambiguous for up to 40% of data sampled for the plasma parameters and bias voltages considered in this study. In this contribution, we employ an autoencoder (AE) to learn a low-dimensional representation of valid data samples. By definition, the coordinates in this space are the features that mostly characterize valid data. Ambiguous data samples are classified in this space using standard classifiers for vectorial data. In this way, we avoid defining complicated threshold rules to identify outliers, which require strong assumptions and introduce biases in the analysis. By removing the outliers that are identified in the latent low-dimensional space of the AE, we find that the average conductive and convective radial heat fluxes are between approximately 5% and 15% lower as when removing outliers identified by threshold values. For contributions to the radial heat flux due to triple correlations, the difference is up to 40%.

In this work we apply and expand on a recently introduced outlier detection algorithm that is based on an unsupervised random forest. We use the algorithm to calculate a similarity measure for stellar spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). We show that the similarity measure traces non-trivial physical properties and contains information about complex structures in the data. We use it for visualization and clustering of the dataset, and discuss its ability to find groups of highly similar objects, including spectroscopic twins. Using the similarity matrix to search the dataset for objects allows us to find objects that are impossible to find using their best fitting model parameters. This includes extreme objects for which the models fail, and rare objects that are outside the scope of the model. We use the similarity measure to detect outliers in the dataset, and find a number of previously unknown Be-type stars, spectroscopic binaries, carbon rich stars, young stars, and a few that we cannot interpret. Our work further demonstrates the potential for scientific discovery when combining machine learning methods with modern survey data. Cone search capability for table J/MNRAS/476/2117/apogeenn (Nearest neighbors APOGEE IDs)

The spatial signature of microevolutionary processes structuring genetic variation may play an important role in the detection of loci under selection. However, the spatial location of samples has not yet been used to quantify this. Here, we present a new two-step method of spatial outlier detection at the individual and deme levels using the power spectrum of Moran eigenvector maps (MEM). The MEM power spectrum quantifies how the variation in a variable, such as the frequency of an allele at a SNP locus, is distributed across a range of spatial scales defined by MEM spatial eigenvectors. The first step (Moran spectral outlier detection: MSOD) uses genetic and spatial information to identify outlier loci by their unusual power spectrum. The second step uses Moran spectral randomization (MSR) to test the association between outlier loci and environmental predictors, accounting for spatial autocorrelation. Using simulated data from two published papers, we tested this two-step method in different scenarios of landscape configuration, selection strength, dispersal capacity and sampling design. Under scenarios that included spatial structure, MSOD alone was sufficient to detect outlier loci at the individual and deme levels without the need for incorporating environmental predictors. Follow-up with MSR generally reduced (already low) false-positive rates, though in some cases led to a reduction in power. The results were surprisingly robust to differences in sample size and sampling design. Our method represents a new tool for detecting potential loci under selection with individual-based and population-based sampling by leveraging spatial information that has hitherto been neglected.

Here are six files that provide details for all 44,120 identified single nucleotide polymorphisms (SNPs) or the 215 outlier SNPs associated with the evolution of rapid character displacement among replicate islands with (2Spp) and without competition (1Spp) between two Anolis species. On 2Spp islands, A. carolinensis occurs higher in trees and have evolved larger toe pads. Among 1Spp and 2Spp island populations, we identify 44,120 SNPs, with 215-outlier SNPs with improbably large FST values, low nucleotide variation, greater linkage than expected, and these SNPs are enriched for animal walking behavior. Thus, we conclude that these 215-outliers are evolving by natural selection in response to the phenotypic convergent evolution of character displacement. There are two, non-mutually exclusive perspective of these nucleotide variants. One is character displacement is convergent: all 215 outlier SNPs are shared among 3 out of 5 2Spp island and 24% of outlier SNPS are shared among all five ...

Identifying and dealing with outliers is an important part of data analysis. A new visualization, the O3 plot, is introduced to aid in the display and understanding of patterns of multivariate outliers. It uses the results of identifying outliers for every possible combination of dataset variables to provide insight into why particular cases are outliers. The O3 plot can be used to compare the results from up to six different outlier identification methods. There is anRpackage OutliersO3 implementing the plot. The article is illustrated with outlier analyses of German demographic and economic data. Supplementary materials for this article are available online.

How can we discover objects we did not know existed within the large data sets that now abound in astronomy? We present an outlier detection algorithm that we developed, based on an unsupervised Random Forest. We test the algorithm on more than two million galaxy spectra from the Sloan Digital Sky Survey and examine the 400 galaxies with the highest outlier score. We find objects which have extreme emission line ratios and abnormally strong absorption lines, objects with unusual continua, including extremely reddened galaxies. We find galaxy-galaxy gravitational lenses, double-peaked emission line galaxies and close galaxy pairs. We find galaxies with high ionization lines, galaxies that host supernovae and galaxies with unusual gas kinematics. Only a fraction of the outliers we find were reported by previous studies that used specific and tailored algorithms to find a single class of unusual objects. Our algorithm is general and detects all of these classes, and many more, regardless of what makes them peculiar. It can be executed on imaging, time series and other spectroscopic data, operates well with thousands of features, is not sensitive to missing values and is easily parallelizable.

DISTRIBUTED ANOMALY DETECTION USING SATELLITE DATA FROM MULTIPLE MODALITIES KANISHKA BHADURI, KAMALIKA DAS, AND PETR VOTAVA** Abstract. There has been a tremendous increase in the volume of Earth Science data over the last decade from modern satellites, in-situ sensors and different climate models. All these datasets need to be co-analyzed for finding interesting patterns or for searching for extremes or outliers. Information extraction from such rich data sources using advanced data mining methodologies is a challenging task not only due to the massive volume of data, but also because these datasets ate physically stored at different geographical locations. Moving these petabytes of data over the network to a single location may waste a lot of bandwidth, and can take days to finish. To solve this problem, in this paper, we present a novel algorithm which can identify outliers in the global data without moving all the data to one location. The algorithm is highly accurate (close to 99%) and requires centralizing less than 5% of the entire dataset. We demonstrate the performance of the algorithm using data obtained from the NASA MODerate-resolution Imaging Spectroradiometer (MODIS) satellite images.

Understanding the statistics of fluctuation driven flows in the boundary layer of magnetically confined plasmas is desired to accurately model the lifetime of the vacuum vessel components. Mirror Langmuir probes (MLPs) are a novel diagnostic that uniquely allow us to sample the plasma parameters on a time scale shorter than the characteristic time scale of their fluctuations. Sudden large-amplitude fluctuations in the plasma degrade the precision and accuracy of the plasma parameters reported by MLPs for cases in which the probe bias range is of insufficient amplitude. While some data samples can readily be classified as valid and invalid, we find that such a classification may be ambiguous for up to 40% of data sampled for the plasma parameters and bias voltages considered in this study. In this contribution, we employ an autoencoder (AE) to learn a low-dimensional representation of valid data samples. By definition, the coordinates in this space are the features that mostly characterize valid data. Ambiguous data samples are classified in this space using standard classifiers for vectorial data. In this way, we avoid defining complicated threshold rules to identify outliers, which require strong assumptions and introduce biases in the analysis. By removing the outliers that aremore » identified in the latent low-dimensional space of the AE, we find that the average conductive and convective radial heat fluxes are between approximately 5% and 15% lower as when removing outliers identified by threshold values. For contributions to the radial heat flux due to triple correlations, the difference is up to 40%.« less

The following report outlines the workflow used to optimize your Find Outliers result:Initial Data Assessment.There were 1684 valid input features.POVERTY Properties:Min0.0000Max91.8000Mean18.9902Std. Dev.12.7152There were 22 outlier locations; these will not be used to compute the optimal fixed distance band.Scale of AnalysisThe optimal fixed distance band was based on the average distance to 30 nearest neighbors: 3709.0000 Meters.Outlier AnalysisCreating the random reference distribution with 499 permutations.There are 1155 output features statistically significant based on a FDR correction for multiple testing and spatial dependence.There are 68 statistically significant high outlier features.There are 84 statistically significant low outlier features.There are 557 features part of statistically significant low clusters.There are 446 features part of statistically significant high clusters.OutputPink output features are part of a cluster of high POVERTY values.Light Blue output features are part of a cluster of low POVERTY values.Red output features represent high outliers within a cluster of low POVERTY values.Blue output features represent low outliers within a cluster of high POVERTY values.

Analysis of the Neighborhood Parameter on Outlier Detection Algorithms - Evaluation Tests conducted for the paper: Impact of the Neighborhood Parameter on Outlier Detection Algorithms by F. Iglesias, C. Martínez, T. Zseby Context and methodology A significant number of anomaly detection algorithms base their distance and density estimates on neighborhood parameters (usually referred to as k). The experiments in this repository analyze how five different SoTA algorithms (kNN, LOF, LooP, ABOD and SDO) are affected by variations in k in combination with different alterations that the data may undergo in relation to: cardinality, dimensionality, global outlier ratio, local outlier ratio, layers of density, inliers-outliers density ratio, and zonification. Evaluations are conducted with accuracy measurements (ROC-AUC, adjusted Average Precision, and Precision at n) and runtimes. This repository is framed within the research on the following domains: algorithm evaluation, outlier detection, anomaly detection, unsupervised learning, machine learning, data mining, data analysis. Datasets and algorithms can be used for experiment replication and for further evaluation and comparison. Technical details Experiments are in Python 3 (tested with v3.9.6). Provided scripts generate all data and results. We keep them in the repo for the sake of comparability and replicability. The file and folder structure is as follows: results_datasets_scores.zip contains all results and plots as shown in the paper, also the generated datasets and files with anomaly dependencies.sh for installing required Python packages in a clean environment. generate_data.py creates experimental datasets. outdet.py runs outlier detection with ABOD, kNN, LOF, LoOP and SDO over the collection of datasets. indices.py contains functions implementing accuracy indices. explore_results.py parses results obtained with outlier detection algorithms to create comparison plots and a table with optimal ks. test_kfc.py rusn KFC tests for finding the optimal k in a collection of datasets. It requires kfc.py, which is not included in this repo and must be downloaded from https://github.com/TimeIsAFriend/KFC. kfc.py implements the KFCS and KFCR methods for finding the optimal k as presented in: [1] explore_kfc.py parses results obtained with KFCS and KFCR methods to create latex tables. README.md provides explanations and step by step instructions for replication. References [1] Jiawei Yang, Xu Tan, Sylwan Rahardja, Outlier detection: How to Select k for k-nearest-neighbors-based outlier detectors, Pattern Recognition Letters, Volume 174, 2023, Pages 112-117, ISSN 0167-8655, https://doi.org/10.1016/j.patrec.2023.08.020. License The CC-BY license applies to all data generated with the "generate_data.py" script. All distributed code is under the GNU GPL license.

In the present era of large-scale surveys, big data present new challenges to the discovery process for anomalous data. Such data can be indicative of systematic errors, extreme (or rare) forms of known phenomena, or most interestingly, truly novel phenomena that exhibit as-of-yet unobserved behaviours. In this work, we present an outlier scoring methodology to identify and characterize the most promising unusual sources to facilitate discoveries of such anomalous data. We have developed a data mining method based on k-nearest neighbour distance in feature space to efficiently identify the most anomalous light curves. We test variations of this method including using principal components of the feature space, removing select features, the effect of the choice of k, and scoring to subset samples. We evaluate the performance of our scoring on known object classes and find that our scoring consistently scores rare (<1000) object classes higher than common classes. We have applied scoring to all long cadence light curves of Quarters 1-17 of Kepler's prime mission and present outlier scores for all 2.8 million light curves for the roughly 200k objects.

BackgroundMeta-analysis of gene expression microarray datasets presents significant challenges for statistical analysis. We developed and validated a new bioinformatic method for the identification of genes upregulated in subsets of samples of a given tumour type (‘outlier genes’), a hallmark of potential oncogenes. MethodologyA new statistical method (the gene tissue index, GTI) was developed by modifying and adapting algorithms originally developed for statistical problems in economics. We compared the potential of the GTI to detect outlier genes in meta-datasets with four previously defined statistical methods, COPA, the OS statistic, the t-test and ORT, using simulated data. We demonstrated that the GTI performed equally well to existing methods in a single study simulation. Next, we evaluated the performance of the GTI in the analysis of combined Affymetrix gene expression data from several published studies covering 392 normal samples of tissue from the central nervous system, 74 astrocytomas, and 353 glioblastomas. According to the results, the GTI was better able than most of the previous methods to identify known oncogenic outlier genes. In addition, the GTI identified 29 novel outlier genes in glioblastomas, including TYMS and CDKN2A. The over-expression of these genes was validated in vivo by immunohistochemical staining data from clinical glioblastoma samples. Immunohistochemical data were available for 65% (19 of 29) of these genes, and 17 of these 19 genes (90%) showed a typical outlier staining pattern. Furthermore, raltitrexed, a specific inhibitor of TYMS used in the therapy of tumour types other than glioblastoma, also effectively blocked cell proliferation in glioblastoma cell lines, thus highlighting this outlier gene candidate as a potential therapeutic target. Conclusions/SignificanceTaken together, these results support the GTI as a novel approach to identify potential oncogene outliers and drug targets. The algorithm is implemented in an R package (Text S1).