MNIST database

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Sample images from MNIST test dataset MnistExamplesModified.png
Sample images from MNIST test dataset

The MNIST database (Modified National Institute of Standards and Technology database [1] ) is a large database of handwritten digits that is commonly used for training various image processing systems. [2] [3] The database is also widely used for training and testing in the field of machine learning. [4] [5] It was created by "re-mixing" the samples from NIST's original datasets. [6] The creators felt that since NIST's training dataset was taken from American Census Bureau employees, while the testing dataset was taken from American high school students, it was not well-suited for machine learning experiments. [7] Furthermore, the black and white images from NIST were normalized to fit into a 28x28 pixel bounding box and anti-aliased, which introduced grayscale levels. [7]

Contents

The MNIST database contains 60,000 training images and 10,000 testing images. [8] Half of the training set and half of the test set were taken from NIST's training dataset, while the other half of the training set and the other half of the test set were taken from NIST's testing dataset. [9] The original creators of the database keep a list of some of the methods tested on it. [7] In their original paper, they use a support-vector machine to get an error rate of 0.8%. [10]

Extended MNIST (EMNIST) is a newer dataset developed and released by NIST to be the (final) successor to MNIST. [11] [12] MNIST included images only of handwritten digits. EMNIST includes all the images from NIST Special Database 19, which is a large database of handwritten uppercase and lower case letters as well as digits. [13] [14] The images in EMNIST were converted into the same 28x28 pixel format, by the same process, as were the MNIST images. Accordingly, tools which work with the older, smaller, MNIST dataset will likely work unmodified with EMNIST.

History

The set of images in the MNIST database was created in 1994 [15] as a combination of two of NIST's databases: Special Database 1 and Special Database 3. Special Database 1 and Special Database 3 consist of digits written by high school students and employees of the United States Census Bureau, respectively. [7]

The original dataset was a set of 128x128 binary images, processed into 28x28 grayscale images. There were originally 60k samples in both the training set and the testing set, but 50k of the testing set were discarded. Refer to [16] for a detailed history and a reconstruction of the discarded testing set.

Performance

Some researchers have achieved "near-human performance" on the MNIST database, using a committee of neural networks; in the same paper, the authors achieve performance double that of humans on other recognition tasks. [17] The highest error rate listed [7] on the original website of the database is 12 percent, which is achieved using a simple linear classifier with no preprocessing. [10]

In 2004, a best-case error rate of 0.42 percent was achieved on the database by researchers using a new classifier called the LIRA, which is a neural classifier with three neuron layers based on Rosenblatt's perceptron principles. [18]

Some researchers have tested artificial intelligence systems using the database put under random distortions. The systems in these cases are usually neural networks and the distortions used tend to be either affine distortions or elastic distortions. [7] Sometimes, these systems can be very successful; one such system achieved an error rate on the database of 0.39 percent. [19]

In 2011, an error rate of 0.27 percent, improving on the previous best result, was reported by researchers using a similar system of neural networks. [20] In 2013, an approach based on regularization of neural networks using DropConnect has been claimed to achieve a 0.21 percent error rate. [21] In 2016, the single convolutional neural network best performance was 0.25 percent error rate. [22] As of August 2018, the best performance of a single convolutional neural network trained on MNIST training data using no data augmentation is 0.25 percent error rate. [22] [23] Also, the Parallel Computing Center (Khmelnytskyi, Ukraine) obtained an ensemble of only 5 convolutional neural networks which performs on MNIST at 0.21 percent error rate. [24] [25] Some images in the testing dataset are barely readable and may prevent reaching test error rates of 0%. [26] In 2018, researchers from Department of System and Information Engineering, University of Virginia announced 0.18% error with simultaneous stacked three kind of neural networks (fully connected, recurrent and convolution neural networks). [27]

Classifiers

This is a table of some of the machine learning methods used on the dataset and their error rates, by type of classifier:

TypeClassifierDistortion Preprocessing Error rate (%)
Linear classifier Pairwise linear classifier NoneDeskewing7.6 [10]
K-Nearest Neighbors K-NN with rigid transformationsNoneNone0.96 [28]
K-Nearest Neighbors K-NN with non-linear deformation (P2DHMDM)NoneShiftable edges0.52 [29]
Boosted Stumps Product of stumps on Haar features NoneHaar features0.87 [30]
Non-linear classifier40 PCA + quadratic classifierNoneNone3.3 [10]
Random Forest Fast Unified Random Forests for Survival, Regression, and Classification (RF-SRC) [31] NoneSimple statistical pixel importance2.8 [32]
Support-vector machine (SVM)Virtual SVM, deg-9 poly, 2-pixel jitteredNoneDeskewing0.56 [33]
Neural network 2-layer 784-800-10NoneNone1.6 [34]
Neural network 2-layer 784-800-10Elastic distortionsNone0.7 [34]
Deep neural network (DNN)6-layer 784-2500-2000-1500-1000-500-10Elastic distortionsNone0.35 [35]
Convolutional neural network (CNN)6-layer 784-40-80-500-1000-2000-10NoneExpansion of the training data0.31 [36]
Convolutional neural network 6-layer 784-50-100-500-1000-10-10NoneExpansion of the training data0.27 [37]
Convolutional neural network (CNN)13-layer 64-128(5x)-256(3x)-512-2048-256-256-10NoneNone0.25 [22]
Convolutional neural network Committee of 35 CNNs, 1-20-P-40-P-150-10Elastic distortionsWidth normalizations0.23 [17]
Convolutional neural network Committee of 5 CNNs, 6-layer 784-50-100-500-1000-10-10NoneExpansion of the training data0.21 [24] [25]
Random Multimodel Deep Learning (RMDL)10 NN-10 RNN - 10 CNNNoneNone0.18 [27]
Convolutional neural network Committee of 20 CNNS with Squeeze-and-Excitation Networks [38] None Data augmentation 0.17 [39]
Convolutional neural network Ensemble of 3 CNNs with varying kernel sizesNone Data augmentation consisting of rotation and translation0.09 [40]

See also

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References

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  6. ↑ Grother, Patrick J. "NIST Special Database 19 - Handprinted Forms and Characters Database" (PDF). National Institute of Standards and Technology .
  7. 1 2 3 4 5 6 LeCun, Yann; Cortez, Corinna; Burges, Christopher C.J. "The MNIST Handwritten Digit Database". Yann LeCun's Website yann.lecun.com. Retrieved 30 April 2020.
  8. ↑ Kussul, Ernst; Baidyk, Tatiana (2004). "Improved method of handwritten digit recognition tested on MNIST database". Image and Vision Computing. 22 (12): 971–981. doi:10.1016/j.imavis.2004.03.008.
  9. ↑ Zhang, Bin; Srihari, Sargur N. (2004). "Fast k-Nearest Neighbor Classification Using Cluster-Based Trees" (PDF). IEEE Transactions on Pattern Analysis and Machine Intelligence. 26 (4): 525–528. doi:10.1109/TPAMI.2004.1265868. PMID   15382657. S2CID   6883417 . Retrieved 20 April 2020.
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  11. ↑ NIST (4 April 2017). "The EMNIST Dataset". NIST . Retrieved 11 April 2022.
  12. ↑ NIST (27 August 2010). "NIST Special Database 19". NIST . Retrieved 11 April 2022.
  13. ↑ Cohen, G.; Afshar, S.; Tapson, J.; van Schaik, A. (2017). "EMNIST: an extension of MNIST to handwritten letters". arXiv: 1702.05373 [cs.CV].
  14. ↑ Cohen, G.; Afshar, S.; Tapson, J.; van Schaik, A. (2017). "EMNIST: an extension of MNIST to handwritten letters". arXiv: 1702.05373v1 [cs.CV].
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  18. ↑ Kussul, Ernst; Tatiana Baidyk (2004). "Improved method of handwritten digit recognition tested on MNIST database" (PDF). Image and Vision Computing. 22 (12): 971–981. doi:10.1016/j.imavis.2004.03.008. Archived from the original (PDF) on 21 September 2013. Retrieved 20 September 2013.
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  21. ↑ Wan, Li; Matthew Zeiler; Sixin Zhang; Yann LeCun; Rob Fergus (2013). Regularization of Neural Network using DropConnect. International Conference on Machine Learning(ICML).
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  31. ↑ "RandomForestSRC: Fast Unified Random Forests for Survival, Regression, and Classification (RF-SRC)". 21 January 2020.
  32. ↑ "Mehrad Mahmoudian / MNIST with RandomForest".
  33. ↑ Decoste, Dennis; Schölkopf, Bernhard (2002). "Training Invariant Support Vector Machines". Machine Learning. 46 (1–3): 161–190. doi: 10.1023/A:1012454411458 . ISSN   0885-6125. OCLC   703649027.
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  38. ↑ Hu, Jie; Shen, Li; Albanie, Samuel; Sun, Gang; Wu, Enhua (2019). "Squeeze-and-Excitation Networks". IEEE Transactions on Pattern Analysis and Machine Intelligence. 42 (8): 2011–2023. arXiv: 1709.01507 . doi:10.1109/TPAMI.2019.2913372. PMID   31034408. S2CID   140309863.
  39. ↑ "GitHub - Matuzas77/MNIST-0.17: MNIST classifier with average 0.17% error". GitHub . 25 February 2020.
  40. ↑ An, Sanghyeon; Lee, Minjun; Park, Sanglee; Yang, Heerin; So, Jungmin (2020-10-04). "An Ensemble of Simple Convolutional Neural Network Models for MNIST Digit Recognition". arXiv: 2008.10400 [cs.CV].

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