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

The zip files contains 12338 datasets for outlier detection investigated in the following papers:
(1) Instance space analysis for unsupervised outlier detection Authors : Sevvandi Kandanaarachchi, Mario A. Munoz, Kate Smith-Miles
(2) On normalization and algorithm selection for unsupervised outlier detection Authors : Sevvandi Kandanaarachchi, Mario A. Munoz, Rob J. Hyndman, Kate Smith-Miles

Some of these datasets were originally discussed in the paper:

On the evaluation of unsupervised outlier detection:measures, datasets and an empirical studyAuthors : G. O. Campos, A, Zimek, J. Sander, R. J.G.B. Campello, B. Micenkova, E. Schubert, I. Assent, M.E. Houle.

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.

📁 Files Included: Outlier_Loan_datase.csv – Raw dataset with outliers `.Final_Outliers_clean_dataset.csv (IQR + Z-score)

This dataset is designed for practicing outlier detection and data cleaning techniques.
It includes both the original (uncleaned) and cleaned versions of a financial dataset.

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.

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.

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 HDoutliers algorithm is a powerful unsupervised algorithm for detecting anomalies in high-dimensional data, with a strong theoretical foundation. However, it suffers from some limitations that significantly hinder its performance level, under certain circumstances. In this article, we propose an algorithm that addresses these limitations. We define an anomaly as an observation where its k-nearest neighbor distance with the maximum gap is significantly different from what we would expect if the distribution of k-nearest neighbors with the maximum gap is in the maximum domain of attraction of the Gumbel distribution. An approach based on extreme value theory is used for the anomalous threshold calculation. Using various synthetic and real datasets, we demonstrate the wide applicability and usefulness of our algorithm, which we call the stray algorithm. We also demonstrate how this algorithm can assist in detecting anomalies present in other data structures using feature engineering. We show the situations where the stray algorithm outperforms the HDoutliers algorithm both in accuracy and computational time. This framework is implemented in the open source R package stray. Supplementary materials for this article are available online.

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.

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

Dataset

This dataset was created by Omsingh Bais

Contents

The dataset used for outlier detection on sensor data from temperature and humidity sensors deployed in sensorized farms and manufacturing units on Purdue University's campus.

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.

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.

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. The categories are available in the dataset and in the metadata.
• 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.
• Suitable for root cause analysis. In addition to the anomaly category, the time series channel in which the anomaly first developed itself is recorded and made available as part of the metadata. This can be useful to evaluate the performance of algorithm to trace back anomalies to the right root cause channel.
• Affected channels. In addition to the knowledge of the root cause channel in which the anomaly first developed itself, we provide information of channels possibly affected by the anomaly. This can also be useful to evaluate the explainability of anomaly detection systems which may point out to the anomalous channels (root cause and affected).
• 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.

Change Log

Version 2

• Metadata: we include a metadata.csv with information about:
  • Anomaly categories
  • Root cause channel (signal in which the anomaly is first visible)
  • Affected channel (signal in which the anomaly might propagate) through coupled system dynamics
• Removal of anomaly overlaps: version 1 contained anomalies which overlapped with each other resulting in only 190 distinct anomalous segments. Now, there are no more anomaly overlaps.
• Two data files: CSV and parquet for convenience.

[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.

Vision Based Building Energy Data Outlier Detection

## Overview

Vision Based Building Energy Data Outlier Detection is a dataset for object detection tasks - it contains 11785 annotations for 2,159 images.

## Getting Started

You can download this dataset for use within your own projects, or fork it into a workspace on Roboflow to create your own model.

  ## License

  This dataset is available under the [CC BY 4.0 license](https://creativecommons.org/licenses/CC BY 4.0).

Consider a scenario in which the data owner has some private or sensitive data and wants a data miner to access them 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 their release to the data miners. Previous works 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 data sets. 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. The experiments conducted on real-life data sets demonstrate the effectiveness of the approach.

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.