Outliers can be more problematic in longitudinal data than in independent observations due to the correlated nature of such data. It is common practice to discard outliers as they are typically regarded as a nuisance or an aberration in the data. However, outliers can also convey meaningful information concerning potential model misspecification, and ways to modify and improve the model. Moreover, outliers that occur among the latent variables (innovative outliers) have distinct characteristics compared to those impacting the observed variables (additive outliers), and are best evaluated with different test statistics and detection procedures. We demonstrate and evaluate the performance of an outlier detection approach for multi-subject state-space models in a Monte Carlo simulation study, with corresponding adaptations to improve power and reduce false detection rates. Furthermore, we demonstrate the empirical utility of the proposed approach using data from an ecological momentary assessment study of emotion regulation together with an open-source software implementation of the procedures.

The problem of distance-based outlier detection is difficult to solve efficiently in very large datasets because of potential quadratic time complexity. We address this problem and develop sequential and distributed algorithms that are significantly more efficient than state-of-the-art methods while still guaranteeing the same outliers. By combining simple but effective indexing and disk block accessing techniques, we have developed a sequential algorithm iOrca that is up to an order-of-magnitude faster than the state-of-the-art. The indexing scheme is based on sorting the data points in order of increasing distance from a fixed reference point and then accessing those points based on this sorted order. To speed up the basic outlier detection technique, we develop two distributed algorithms (DOoR and iDOoR) for modern distributed multi-core clusters of machines, connected on a ring topology. The first algorithm passes data blocks from each machine around the ring, incrementally updating the nearest neighbors of the points passed. By maintaining a cutoff threshold, it is able to prune a large number of points in a distributed fashion. The second distributed algorithm extends this basic idea with the indexing scheme discussed earlier. In our experiments, both distributed algorithms exhibit significant improvements compared to the state-of-the-art distributed methods.

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. This standard “detect-and-forget” approach has been shown to be problematic, and in this paper we highlight the fact that it can lead to invalid inference and show how recently developed tools in selective inference can be used to properly account for outlier detection and removal. Our inferential procedures apply to a general class of outlier removal procedures that includes several of the most commonly used approaches. We conduct simulations to corroborate the theoretical results, and we apply our method to three real data sets to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.

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Anomaly Detection Market Size 2024-2028

The anomaly detection market size is forecast to increase by USD 3.71 billion at a CAGR of 13.63% between 2023 and 2028. Anomaly detection is a critical aspect of cybersecurity, particularly in sectors like healthcare where abnormal patient conditions or unusual network activity can have significant consequences. The market for anomaly detection solutions is experiencing significant growth due to several factors. Firstly, the increasing incidence of internal threats and cyber frauds has led organizations to invest in advanced tools for detecting and responding to anomalous behavior. Secondly, the infrastructural requirements for implementing these solutions are becoming more accessible, making them a viable option for businesses of all sizes. Data science and machine learning algorithms play a crucial role in anomaly detection, enabling accurate identification of anomalies and minimizing the risk of incorrect or misleading conclusions.

However, data quality is a significant challenge in this field, as poor quality data can lead to false positives or false negatives, undermining the effectiveness of the solution. Overall, the market for anomaly detection solutions is expected to grow steadily in the coming years, driven by the need for enhanced cybersecurity and the increasing availability of advanced technologies.

What will be the Anomaly Detection Market Size During the Forecast Period?

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Anomaly detection, also known as outlier detection, is a critical data analysis technique used to identify observations or events that deviate significantly from the normal behavior or expected patterns in data. These deviations, referred to as anomalies or outliers, can indicate infrastructure failures, breaking changes, manufacturing defects, equipment malfunctions, or unusual network activity. In various industries, including manufacturing, cybersecurity, healthcare, and data science, anomaly detection plays a crucial role in preventing incorrect or misleading conclusions. Artificial intelligence and machine learning algorithms, such as statistical tests (Grubbs test, Kolmogorov-Smirnov test), decision trees, isolation forest, naive Bayesian, autoencoders, local outlier factor, and k-means clustering, are commonly used for anomaly detection.

Furthermore, these techniques help identify anomalies by analyzing data points and their statistical properties using charts, visualization, and ML models. For instance, in manufacturing, anomaly detection can help identify defective products, while in cybersecurity, it can detect unusual network activity. In healthcare, it can be used to identify abnormal patient conditions. By applying anomaly detection techniques, organizations can proactively address potential issues and mitigate risks, ensuring optimal performance and security.

Market Segmentation

The market research report provides comprehensive data (region-wise segment analysis), with forecasts and estimates in 'USD billion' for the period 2024-2028, as well as historical data from 2018-2022 for the following segments.

Deployment

  Cloud
  On-premise


Geography

  North America

    US


  Europe

    Germany
    UK


  APAC

    China
    Japan


  South America



  Middle East and Africa

By Deployment Insights

The cloud segment is estimated to witness significant growth during the forecast period. The market is witnessing a notable shift towards cloud-based solutions due to their numerous advantages over traditional on-premises systems. Cloud-based anomaly detection offers breaking changes such as quicker deployment, enhanced flexibility, and scalability, real-time data visibility, and customization capabilities. These features are provided by service providers with flexible payment models like monthly subscriptions and pay-as-you-go, making cloud-based software a cost-effective and economical choice. Anodot, Ltd, Cisco Systems Inc, IBM Corp, and SAS Institute Inc are some prominent companies offering cloud-based anomaly detection solutions in addition to on-premise alternatives. In the context of security threats, architectural optimization, marketing strategies, finance, fraud detection, manufacturing, and defects, equipment malfunctions, cloud-based anomaly detection is becoming increasingly popular due to its ability to provide real-time insights and swift response to anomalies.

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The cloud segment accounted for USD 1.59 billion in 2018 and showed a gradual increase during the forecast period.

Regional Insights

When it comes to Anomaly Detection Market growth, North America is estimated to contribute 37% to the global market during the forecast period. Technavio's analysts have elaborately explained the regional trends and drivers that shape the market during the forecast per

Usage notes

Consider a scenario in which the data owner has some private/sensitive data and wants a data miner to access it for studying important patterns without revealing the sensitive information. Privacy preserving data mining aims to solve this problem by randomly transforming the data prior to its release to data miners. Previous work only considered the case of linear data perturbations — additive, multiplicative or a combination of both for studying the usefulness of the perturbed output. In this paper, we discuss nonlinear data distortion using potentially nonlinear random data transformation and show how it can be useful for privacy preserving anomaly detection from sensitive datasets. We develop bounds on the expected accuracy of the nonlinear distortion and also quantify privacy by using standard definitions. The highlight of this approach is to allow a user to control the amount of privacy by varying the degree of nonlinearity. We show how our general transformation can be used for anomaly detection in practice for two specific problem instances: a linear model and a popular nonlinear model using the sigmoid function. We also analyze the proposed nonlinear transformation in full generality and then show that for specific cases it is distance preserving. A main contribution of this paper is the discussion between the invertibility of a transformation and privacy preservation and the application of these techniques to outlier detection. Experiments conducted on real-life datasets demonstrate the effectiveness of the approach.

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).

Dataset

This dataset was created by Hai Vo

Released under Database: Open Database, Contents: Database Contents

Contents

The Multi-Domain Outlier Detection Dataset contains datasets for conducting outlier detection experiments for four different application domains:

Astrophysics - detecting anomalous observations in the Dark Energy Survey (DES) catalog (data type: feature vectors)

Planetary science - selecting novel geologic targets for follow-up observation onboard the Mars Science Laboratory (MSL) rover (data type: grayscale images)

Earth science: detecting anomalous samples in satellite time series corresponding to ground-truth observations of maize crops (data type: time series/feature vectors)

Fashion-MNIST/MNIST: benchmark task to detect anomalous MNIST images among Fashion-MNIST images (data type: grayscale images)

Each dataset contains a "fit" dataset (used for fitting or training outlier detection models), a "score" dataset (used for scoring samples used to evaluate model performance, analogous to test set), and a label dataset (indicates whether samples in the score dataset are considered outliers or not in the domain of each dataset).

To read more about the datasets and how they are used for outlier detection, or to cite this dataset in your own work, please see the following citation:

Kerner, H. R., Rebbapragada, U., Wagstaff, K. L., Lu, S., Dubayah, B., Huff, E., Lee, J., Raman, V., and Kulshrestha, S. (2022). Domain-agnostic Outlier Ranking Algorithms (DORA)-A Configurable Pipeline for Facilitating Outlier Detection in Scientific Datasets. Under review for Frontiers in Astronomy and Space Sciences.

Additional file 6. Supplemental Table 6: List of genes validated by qRT-PCR with primer sequences, results and DEG status in each analysis strategy.

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 the system-wide health of a fleet of aircraft. The approach taken uses unsupervised clustering of sequences using the normalized length of the longest common subsequence (nLCS) as a similarity measure, followed by detailed outlier analysis to detect anomalies. In this method, an outlier sequence is defined as a sequence that is far away from the cluster centre. We present new algorithms for outlier analysis that provide comprehensible indicators as to why a particular sequence is deemed to be an outlier. The algorithms provide a coherent description to an analyst of the anomalies in the sequence when compared to more normal sequences. In the final section of the paper we demonstrate 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.

The Controlled Anomalies Time Series (CATS) Dataset consists of commands, external stimuli, and telemetry readings of a simulated complex dynamical system with 200 injected anomalies.

The CATS Dataset exhibits a set of desirable properties that make it very suitable for benchmarking Anomaly Detection Algorithms in Multivariate Time Series [1]:

• Multivariate (17 variables) including sensors reading and control signals. It simulates the operational behaviour of an arbitrary complex system including:
  • 4 Deliberate Actuations / Control Commands sent by a simulated operator / controller, for instance, commands of an operator to turn ON/OFF some equipment.
  • 3 Environmental Stimuli / External Forces acting on the system and affecting its behaviour, for instance, the wind affecting the orientation of a large ground antenna.
  • 10 Telemetry Readings representing the observable states of the complex system by means of sensors, for instance, a position, a temperature, a pressure, a voltage, current, humidity, velocity, acceleration, etc.
• 5 million timestamps. Sensors readings are at 1Hz sampling frequency.
  • 1 million nominal observations (the first 1 million datapoints). This is suitable to start learning the "normal" behaviour.
  • 4 million observations that include both nominal and anomalous segments. This is suitable to evaluate both semi-supervised approaches (novelty detection) as well as unsupervised approaches (outlier detection).
• 200 anomalous segments. One anomalous segment may contain several successive anomalous observations / timestamps. Only the last 4 million observations contain anomalous segments.
• Different types of anomalies to understand what anomaly types can be detected by different approaches.
• Fine control over ground truth. As this is a simulated system with deliberate anomaly injection, the start and end time of the anomalous behaviour is known very precisely. In contrast to real world datasets, there is no risk that the ground truth contains mislabelled segments which is often the case for real data.
• Obvious anomalies. The simulated anomalies have been designed to be "easy" to be detected for human eyes (i.e., there are very large spikes or oscillations), hence also detectable for most algorithms. It makes this synthetic dataset useful for screening tasks (i.e., to eliminate algorithms that are not capable to detect those obvious anomalies). However, during our initial experiments, the dataset turned out to be challenging enough even for state-of-the-art anomaly detection approaches, making it suitable also for regular benchmark studies.
• Context provided. Some variables can only be considered anomalous in relation to other behaviours. A typical example consists of a light and switch pair. The light being either on or off is nominal, the same goes for the switch, but having the switch on and the light off shall be considered anomalous. In the CATS dataset, users can choose (or not) to use the available context, and external stimuli, to test the usefulness of the context for detecting anomalies in this simulation.
• Pure signal ideal for robustness-to-noise analysis. The simulated signals are provided without noise: while this may seem unrealistic at first, it is an advantage since users of the dataset can decide to add on top of the provided series any type of noise and choose an amplitude. This makes it well suited to test how sensitive and robust detection algorithms are against various levels of noise.
• No missing data. You can drop whatever data you want to assess the impact of missing values on your detector with respect to a clean baseline.

[1] Example Benchmark of Anomaly Detection in Time Series: “Sebastian Schmidl, Phillip Wenig, and Thorsten Papenbrock. Anomaly Detection in Time Series: A Comprehensive Evaluation. PVLDB, 15(9): 1779 - 1797, 2022. doi:10.14778/3538598.3538602”

About Solenix

Solenix is an international company providing software engineering, consulting services and software products for the space market. Solenix is a dynamic company that brings innovative technologies and concepts to the aerospace market, keeping up to date with technical advancements and actively promoting spin-in and spin-out technology activities. We combine modern solutions which complement conventional practices. We aspire to achieve maximum customer satisfaction by fostering collaboration, constructivism, and flexibility.

The results represent experiments on four datasets based on 20 simulated experiments. The proposed method (NewAlgo) produces the best overall results.

Dataset Card for "cifar10-outlier"

📚 This dataset is an enriched version of the CIFAR-10 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 Spaces running Spotlight with this dataset here:

Full Version (High hardware requirement)… See the full description on the dataset page: https://huggingface.co/datasets/renumics/cifar10-outlier.

Dataset

This dataset was created by Abubacker S

Released under CC0: Public Domain

Contents

The results represent experiments on a single real-life dataset. The proposed method (NewAlgo) produces the best overall results.

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.

Usage noteVCF datasets were generated “de novo” with Stacks V.2.52 from reads produce by the protocols used and provided in the manuscript.Sample associated metadata were collected during field sampling.# File descriptionMetadata fileMetadata csv file about samples information.This contains information about the 486 samples during the field work. (cruise part, basin, locality, sample site ,depth and the associated name used in the analyses)- SampleID : Sample ID of all individual- Cruise_part : part of the sampling cruise - Individual : Individual name of the sample- Sample_name : Sample name used in the ddRad-seq libraries- Sample_site : ID of the sampling site (within the locality)- Locality : Name of the locality or hydrothermal field for all samples - Locality2 : Name of the locality or hydrothermal for only Chubacarc sample- Basin : Name of the basin - Depth(m) : Depth of the sampling sites in meter- Cruise : Origin (cruise or collection) of the sample (SH...

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

Additional file 2.