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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 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.
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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.
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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.
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.
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.
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).
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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.
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.
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
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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.
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
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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]:
[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.
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1) Data Introduction • The Dynamic Apparel Sales with Anomalies Dataset is based on 100,000 sales transaction data from the fashion industry, including extreme outliers, missing values, and sales_categories, reflecting the different data characteristics of real retail environments.
2) Data Utilization (1) Dynamic Apparel Sales with Anomalies Dataset has characteristics that: • This dataset consists of nine categorical variables and 10 numerical variables, including product name, brand, gender clothing, price, discount rate, inventory level, and customer behavior, making it suitable for analyzing product and customer characteristics. (2) Dynamic Apparel Sales with Anomalies Dataset can be used to: • Sales anomaly detection and quality control: Transaction data with outliers and missing values can be used to detect outliers, manage quality, refine data, and develop outlier processing techniques. • Sales Forecast and Customer Analysis Modeling: Based on a variety of product and customer characteristics, it can be used to support data-driven decision-making, such as machine learning-based sales forecasting, customer segmentation, and customized marketing strategies.
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Tissue deformation is a critical issue in soft-tissue surgery, particularly during tumor resection, as it causes landmark displacement, complicating tissue orientation. The authors conducted an experimental study on 45 pig head cadavers to simulate tissue deformation, approved by the Mannheim Veterinary Office (DE 08 222 1019 21). We used 3D cameras and head-mounted displays to capture tissue shapes before and after controlled deformation induced by heating. The data were processed using software such as Meshroom, MeshLab, and Blender to create and evaluate 2½D meshes. The dataset includes different levels of deformation, noise, and outliers, generated using the same approach as the SynBench dataset. 1. Deformation_Level: 10 different deformation levels are considered. 0.1 and 0.7 are representing minimum and maximum deformation, respectively. Source and target files are available in each folder. The deformation process is just applied to target files. For simplicity, the corresponding source files to the target ones are available in this folder with the same name, but source ones start with Source_ and the target files start with Target_. The number after Source_ and Target_ represents the primitive object in the “Data” folder. For example, Target_3 represents that this file is generated from object number 3 in the “Data” folder. The two other numbers in the file name represent the percentage number of control points and the width of the Gaussian radial basis function, respectively. 2. Noisy_Data For all available files in the “Deformation_Level” folder (for all deformation levels), Noisy data is generated. They are generated in 4 different noise levels namely, 0.01, 0.02, 0.03, and 0.04 (More explanation about implementation can be found in the paper). The name of the files is the same as the files in the “Deformation_Level” folder. 3. Outlier_Data For all available files in the “Deformation_Level” folder (for all deformation levels), data with outliers is generated. They are generated in different outlier levels, in 5 categories, namely, 5%, 15%, 25%, 35%, and 45% (More explanation about implementation can be found in the paper). The name of the files is the same as the files in the “Deformation_Level” folder. Furthermore, for each file, there is one additional file with the same name but is started with “Outlier_”. This represents a matrix with the coordinates of outliers. Then, it would be possible to use these files as benchmarks to check the validity of future algorithms. Additional notes: Considering the fact that all challenges are generated under small to large deformation levels, the DeformedTissue dataset makes it possible for users to select their desired data based on the ability of their proposed method, to show how robust to complex challenges their methods are.
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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.
201_Cannon_FILT_altLow_STIM.matpreprocessed EEG data from subject 201203_Cannon_FILT_altLow_STIM.matCleaned EEG data from participant 203204_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 204205_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 205206_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 206207_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 207210_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 210211_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for subject 211212_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for participant 212213_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for participant 213214_Cannon_FILT_altLow_STIM.mat215_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for participant 215216_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for participant 216229_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for participant 229233_Cannon_FILT_altLow_STIM.matpreprocessed EEG data for particip...
The original ionosphere dataset from UCI machine learning repository is a binary classification dataset with dimensionality 34. There is one attribute having values all zeros, which is discarded. So the total number of dimensions are 33. The ‘bad’ class is considered as outliers class and the ‘good’ class as inliers.
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Title: Gender Classification Dataset
Description: This dataset contains anonymized information on height, weight, age, and gender of 10,000 individuals. The data is equally distributed between males and females, with 5,000 samples for each gender. The purpose of this dataset is to provide a comprehensive sample for studies and analyses related to physical attributes and demographics.
Content: The CSV file contains the following columns:
Gender: The gender of the individual (Male/Female) Height: The height of the individual in centimeters Weight: The weight of the individual in kilograms Age: The age of the individual in years
License: This dataset is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND 4.0) license. This means you are free to share the data, provided that you attribute the source, do not use it for commercial purposes, and do not distribute modified versions of the data.
Usage:
This dataset can be used for: - Analyzing the distribution of height, weight, and age across genders - Developing and testing machine learning models for predicting physical attributes - Educational purposes in statistics and data science courses
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211 estimates of the social cost of carbon are included in a meta-analysis. The results confirm that a lower discount rate implies a higher estimate; and that higher estimates are found in the gray literature. It is also found that there is a downward trend in the economic impact estimates of the climate; that the Stern Review’s estimates of the social cost of carbon is an outlier; and that the right tail of the distribution is fat. There is a fair chance that the annual climate liability exceeds the annual income of many people.
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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