Here we present a dataset, MNIST4OD, of large size (number of dimensions and number of instances) suitable for Outliers Detection task.The dataset is based on the famous MNIST dataset (http://yann.lecun.com/exdb/mnist/).We build MNIST4OD in the following way:To distinguish between outliers and inliers, we choose the images belonging to a digit as inliers (e.g. digit 1) and we sample with uniform probability on the remaining images as outliers such as their number is equal to 10% of that of inliers. We repeat this dataset generation process for all digits. For implementation simplicity we then flatten the images (28 X 28) into vectors.Each file MNIST_x.csv.gz contains the corresponding dataset where the inlier class is equal to x.The data contains one instance (vector) in each line where the last column represents the outlier label (yes/no) of the data point. The data contains also a column which indicates the original image class (0-9).See the following numbers for a complete list of the statistics of each datasets ( Name | Instances | Dimensions | Number of Outliers in % ):MNIST_0 | 7594 | 784 | 10MNIST_1 | 8665 | 784 | 10MNIST_2 | 7689 | 784 | 10MNIST_3 | 7856 | 784 | 10MNIST_4 | 7507 | 784 | 10MNIST_5 | 6945 | 784 | 10MNIST_6 | 7564 | 784 | 10MNIST_7 | 8023 | 784 | 10MNIST_8 | 7508 | 784 | 10MNIST_9 | 7654 | 784 | 10

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).

Cylindrical data are bivariate data formed from the combination of circular and linear variables. Identifying outliers is a crucial step in any data analysis work. This paper proposes a new distribution-free procedure to detect outliers in cylindrical data using the Mahalanobis distance concept. The use of Mahalanobis distance incorporates the correlation between the components of the cylindrical distribution, which had not been accounted for in the earlier papers on outlier detection in cylindrical data. The threshold for declaring an observation to be an outlier can be obtained via parametric or non-parametric bootstrap, depending on whether the underlying distribution is known or unknown. The performance of the proposed method is examined via extensive simulations from the Johnson-Wehrly distribution. The proposed method is applied to two real datasets, and the outliers are identified in those datasets.

The following report outlines the workflow used to optimize your Find Outliers result:Initial Data Assessment.There were 137 valid input features.There were 4 outlier locations; these will not be used to compute the polygon cell size.Incident AggregationThe polygon cell size was 49251.0000 Meters.The aggregation process resulted in 72 weighted areas.Incident Count Properties:Min1.0000Max21.0000Mean1.9028Std. Dev.2.4561Scale of AnalysisThe optimal fixed distance band selected was based on peak clustering found at 94199.9365 Meters.Outlier AnalysisCreating the random reference distribution with 499 permutations.There are 3 output features statistically significant based on a FDR correction for multiple testing and spatial dependence.There are 2 statistically significant high outlier features.There are 0 statistically significant low outlier features.There are 0 features part of statistically significant low clusters.There are 1 features part of statistically significant high clusters.OutputPink output features are part of a cluster of high values.Light Blue output features are part of a cluster of low values.Red output features represent high outliers within a cluster of low values.Blue output features represent low outliers within a cluster of high values.

The zip files contains 12338 datasets for outlier detection investigated in the following papers:

ensuring accurate representations in spatial and temporal data analyses.

The following report outlines the workflow used to optimize your Find Outliers result:Initial Data Assessment.There were 721 valid input features.GRM Properties:Min0.0000Max157.0200Mean9.1692Std. Dev.8.4220There were 4 outlier locations; these will not be used to compute the optimal fixed distance band.Scale of AnalysisThe optimal fixed distance band selected was based on peak clustering found at 1894.5039 Meters.Outlier AnalysisCreating the random reference distribution with 499 permutations.There are 248 output features statistically significant based on a FDR correction for multiple testing and spatial dependence.There are 30 statistically significant high outlier features.There are 7 statistically significant low outlier features.There are 202 features part of statistically significant low clusters.There are 9 features part of statistically significant high clusters.OutputPink output features are part of a cluster of high GRM values.Light Blue output features are part of a cluster of low GRM values.Red output features represent high outliers within a cluster of low GRM values.Blue output features represent low outliers within a cluster of high GRM values.

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.

OSU_SnowCourse Summary: Manual snow course observations were collected over WY 2012-2014 from four paired forest-open sites chosen to span a broad elevation range. Study sites were located in the upper McKenzie (McK) River watershed, approximately 100 km east of Corvallis, Oregon, on the western slope of the Cascade Range and in the Middle Fork Willamette (MFW) watershed, located to the south of the McKenzie. The sites were designated based on elevation, with a range of 1110-1480 m. Distributed snow depth and snow water equivalent (SWE) observations were collected via monthly manual snow courses from 1 November through 1 April and bi-weekly thereafter. Snow courses spanned 500 m of forested terrain and 500 m of adjacent open terrain. Snow depth observations were collected approximately every 10 m and SWE was measured every 100 m along the snow courses with a federal snow sampler. These data are raw observations and have not been quality controlled in any way. Distance along the transect was estimated in the field. OSU_SnowDepth Summary: 10-minute snow depth observations collected at OSU met stations in the upper McKenzie River Watershed and the Middle Fork Willamette Watershed during Water Years 2012-2014. Each meterological tower was deployed to represent either a forested or an open area at a particular site, and generally the locations were paired, with a meterological station deployed in the forest and in the open area at a single site. These data were collected in conjunction with manual snow course observations, and the meterological stations were located in the approximate center of each forest or open snow course transect. These data have undergone basic quality control. See manufacturer specifications for individual instruments to determine sensor accuracy. This file was compiled from individual raw data files (named "RawData.txt" within each site and year directory) provided by OSU, along with metadata of site attributes. We converted the Excel-based timestamp (seconds since origin) to a date, changed the NaN flags for missing data to NA, and added site attributes such as site name and cover. We replaced positive values with NA, since snow depth values in raw data are negative (i.e., flipped, with some correction to use the height of the sensor as zero). Thus, positive snow depth values in the raw data equal negative snow depth values. Second, the sign of the data was switched to make them positive. Then, the smooth.m (MATLAB) function was used to roughly smooth the data, with a moving window of 50 points. Third, outliers were removed. All values higher than the smoothed values +10, were replaced with NA. In some cases, further single point outliers were removed. OSU_Met Summary: Raw, 10-minute meteorological observations collected at OSU met stations in the upper McKenzie River Watershed and the Middle Fork Willamette Watershed during Water Years 2012-2014. Each meterological tower was deployed to represent either a forested or an open area at a particular site, and generally the locations were paired, with a meterological station deployed in the forest and in the open area at a single site. These data were collected in conjunction with manual snow course observations, and the meteorological stations were located in the approximate center of each forest or open snow course transect. These stations were deployed to collect numerous meteorological variables, of which snow depth and wind speed are included here. These data are raw datalogger output and have not been quality controlled in any way. See manufacturer specifications for individual instruments to determine sensor accuracy. This file was compiled from individual raw data files (named "RawData.txt" within each site and year directory) provided by OSU, along with metadata of site attributes. We converted the Excel-based timestamp (seconds since origin) to a date, changed the NaN and 7999 flags for missing data to NA, and added site attributes such as site name and cover. OSU_Location Summary: Location Metadata for manual snow course observations and meteorological sensors. These data are compiled from GPS data for which the horizontal accuracy is unknown, and from processed hemispherical photographs. They have not been quality controlled in any way.

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.

Usage notes

These data sets were originally created for the following publications:

M. E. Houle, H.-P. Kriegel, P. Kröger, E. Schubert, A. Zimek
Can Shared-Neighbor Distances Defeat the Curse of Dimensionality?
In Proceedings of the 22nd International Conference on Scientific and Statistical Database Management (SSDBM), Heidelberg, Germany, 2010.

H.-P. Kriegel, E. Schubert, A. Zimek
Evaluation of Multiple Clustering Solutions
In 2nd MultiClust Workshop: Discovering, Summarizing and Using Multiple Clusterings Held in Conjunction with ECML PKDD 2011, Athens, Greece, 2011.

The outlier data set versions were introduced in:

E. Schubert, R. Wojdanowski, A. Zimek, H.-P. Kriegel
On Evaluation of Outlier Rankings and Outlier Scores
In Proceedings of the 12th SIAM International Conference on Data Mining (SDM), Anaheim, CA, 2012.

They are derived from the original image data available at https://aloi.science.uva.nl/

The image acquisition process is documented in the original ALOI work: J. M. Geusebroek, G. J. Burghouts, and A. W. M. Smeulders, The Amsterdam library of object images, Int. J. Comput. Vision, 61(1), 103-112, January, 2005

Additional information is available at: https://elki-project.github.io/datasets/multi_view

The following views are currently available:

Feature type	Description	Files
Object number	Sparse 1000 dimensional vectors that give the true object assignment	objs.arff.gz
RGB color histograms	Standard RGB color histograms (uniform binning)	aloi-8d.csv.gz aloi-27d.csv.gz aloi-64d.csv.gz aloi-125d.csv.gz aloi-216d.csv.gz aloi-343d.csv.gz aloi-512d.csv.gz aloi-729d.csv.gz aloi-1000d.csv.gz
HSV color histograms	Standard HSV/HSB color histograms in various binnings	aloi-hsb-2x2x2.csv.gz aloi-hsb-3x3x3.csv.gz aloi-hsb-4x4x4.csv.gz aloi-hsb-5x5x5.csv.gz aloi-hsb-6x6x6.csv.gz aloi-hsb-7x7x7.csv.gz aloi-hsb-7x2x2.csv.gz aloi-hsb-7x3x3.csv.gz aloi-hsb-14x3x3.csv.gz aloi-hsb-8x4x4.csv.gz aloi-hsb-9x5x5.csv.gz aloi-hsb-13x4x4.csv.gz aloi-hsb-14x5x5.csv.gz aloi-hsb-10x6x6.csv.gz aloi-hsb-14x6x6.csv.gz
Color similiarity	Average similarity to 77 reference colors (not histograms) 18 colors x 2 sat x 2 bri + 5 grey values (incl. white, black)	aloi-colorsim77.arff.gz (feature subsets are meaningful here, as these features are computed independently of each other)
Haralick features	First 13 Haralick features (radius 1 pixel)	aloi-haralick-1.csv.gz
Front to back	Vectors representing front face vs. back faces of individual objects	front.arff.gz
Basic light	Vectors indicating basic light situations	light.arff.gz
Manual annotations	Manually annotated object groups of semantically related objects such as cups	manual1.arff.gz

Outlier Detection Versions

Additionally, we generated a number of subsets for outlier detection:

Feature type	Description	Files
RGB Histograms	Downsampled to 100000 objects (553 outliers)	aloi-27d-100000-max10-tot553.csv.gz aloi-64d-100000-max10-tot553.csv.gz
	Downsampled to 75000 objects (717 outliers)	aloi-27d-75000-max4-tot717.csv.gz aloi-64d-75000-max4-tot717.csv.gz
	Downsampled to 50000 objects (1508 outliers)	aloi-27d-50000-max5-tot1508.csv.gz aloi-64d-50000-max5-tot1508.csv.gz

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

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.

Dataset Card for "mnist-outlier"

📚 This dataset is an enriched version of the MNIST Dataset. The workflow is described in the medium article: Changes of Embeddings during Fine-Tuning of Transformers.

  Explore the Dataset

The open source data curation tool Renumics Spotlight allows you to explorer this dataset. You can find a Hugging Face Space running Spotlight with this dataset here: https://huggingface.co/spaces/renumics/mnist-outlier.

Or you can explorer it locally:… See the full description on the dataset page: https://huggingface.co/datasets/renumics/mnist-outlier.

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%.

There are three files containing Stata data, and do and log-files. These are associated with the empirical models reported in the replication study, “Outlier Analysis: Natural Resources and Immigration Policy,” POLS ONE. Questions or comments regarding these materials should be directed to Seung-Whan Choi, Department of Political Science, University of Illinois at Chicago. His email address is whanchoi@uic.edu and his homepage address is https://whanchoi.people.uic.edu/.

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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

Patterns of multi-locus differentiation (i.e., genomic clines) often extend broadly across hybrid zones and their quantification can help diagnose how species boundaries are shaped by adaptive processes, both intrinsic and extrinsic. In this sense, the transitioning of loci across admixed individuals can be contrasted as a function of the genome-wide trend, in turn allowing an expansion of clinal theory across a much wider array of biodiversity. However, computational tools that serve to interpret and consequently visualize ‘genomic clines’ are limited.

Here, we introduce the ClinePlotR R-package for visualizing genomic clines and detecting outlier loci using output generated by two popular software packages, bgc and Introgress.

ClinePlotR bundles both input generation (i.e, filtering datasets and creating specialized file formats) and output processing (e.g., MCMC thinning and burn-in) with functions that directly facilitate interpretation and hypothesis testing. Tools are also p...

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.