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.

ensuring accurate representations in spatial and temporal data analyses.

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.

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).

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.

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.

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.

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.

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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

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 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%.

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.

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.

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

Kriging with interpolation is widely used in various noise-free areas, such as computer experiments. However, owing to its Gaussian assumption, it is susceptible to outliers, which affects statistical inference, and the resulting conclusions could be misleading. Little work has explored outlier detection for kriging. Therefore, we propose a novel kriging method for simultaneous outlier detection and prediction by introducing a normal-gamma prior, which results in an unbounded penalty on the biases to distinguish outliers from normal data points. We develop a simple and efficient method, avoiding the expensive computation of the Markov chain Monte Carlo algorithm, to simultaneously detect outliers and make a prediction. We establish the true identification property for outlier detection and the consistency of the estimated hyperparameters in kriging under the increasing domain framework as if the number and locations of the outliers were known in advance. Under appropriate regularity conditions, we demonstrate information consistency for prediction in the presence of outliers. Numerical studies and real data examples show that the proposed method generally provides robust analyses in the presence of outliers. Supplementary materials for this article are available online.

Multivariate data are typically represented by a rectangular matrix (table) in which the rows are the objects (cases) and the columns are the variables (measurements). When there are many variables one often reduces the dimension by principal component analysis (PCA), which in its basic form is not robust to outliers. Much research has focused on handling rowwise outliers, that is, rows that deviate from the majority of the rows in the data (e.g., they might belong to a different population). In recent years also cellwise outliers are receiving attention. These are suspicious cells (entries) that can occur anywhere in the table. Even a relatively small proportion of outlying cells can contaminate over half the rows, which causes rowwise robust methods to break down. In this article, a new PCA method is constructed which combines the strengths of two existing robust methods to be robust against both cellwise and rowwise outliers. At the same time, the algorithm can cope with missing values. As of yet it is the only PCA method that can deal with all three problems simultaneously. Its name MacroPCA stands for PCA allowing for Missingness And Cellwise & Rowwise Outliers. Several simulations and real datasets illustrate its robustness. New residual maps are introduced, which help to determine which variables are responsible for the outlying behavior. The method is well-suited for online process control.

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 are 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.

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.

Full title: Mining Distance-Based Outliers in Near Linear Time with Randomization and a Simple Pruning Rule Abstract: Defining outliers by their distance to neighboring examples is a popular approach to finding unusual examples in a data set. Recently, much work has been conducted with the goal of finding fast algorithms for this task. We show that a simple nested loop algorithm that in the worst case is quadratic can give near linear time performance when the data is in random order and a simple pruning rule is used. We test our algorithm on real high-dimensional data sets with millions of examples and show that the near linear scaling holds over several orders of magnitude. Our average case analysis suggests that much of the efficiency is because the time to process non-outliers, which are the majority of examples, does not depend on the size of the data set.

Analyzing sales data is essential for any business looking to make informed decisions and optimize its operations. In this project, we will utilize Microsoft Excel and Power Query to conduct a comprehensive analysis of Superstore sales data. Our primary objectives will be to establish meaningful connections between various data sheets, ensure data quality, and calculate critical metrics such as the Cost of Goods Sold (COGS) and discount values. Below are the key steps and elements of this analysis:

1- Data Import and Transformation:

• Gather and import relevant sales data from various sources into Excel.
• Utilize Power Query to clean, transform, and structure the data for analysis.
• Merge and link different data sheets to create a cohesive dataset, ensuring that all data fields are connected logically.

2- Data Quality Assessment:

• Perform data quality checks to identify and address issues like missing values, duplicates, outliers, and data inconsistencies.
• Standardize data formats and ensure that all data is in a consistent, usable state.

3- Calculating COGS:

• Determine the Cost of Goods Sold (COGS) for each product sold by considering factors like purchase price, shipping costs, and any additional expenses.
• Apply appropriate formulas and calculations to determine COGS accurately.

4- Discount Analysis:

• Analyze the discount values offered on products to understand their impact on sales and profitability.
• Calculate the average discount percentage, identify trends, and visualize the data using charts or graphs.

5- Sales Metrics:

• Calculate and analyze various sales metrics, such as total revenue, profit margins, and sales growth.
• Utilize Excel functions to compute these metrics and create visuals for better insights.

6- Visualization:

• Create visualizations, such as charts, graphs, and pivot tables, to present the data in an understandable and actionable format.
• Visual representations can help identify trends, outliers, and patterns in the data.

7- Report Generation:

• Compile the findings and insights into a well-structured report or dashboard, making it easy for stakeholders to understand and make informed decisions.

Throughout this analysis, the goal is to provide a clear and comprehensive understanding of the Superstore's sales performance. By using Excel and Power Query, we can efficiently manage and analyze the data, ensuring that the insights gained contribute to the store's growth and success.