资源数据集MNIST 手写数字图像数据

MNIST 手写数字图像数据

2019-11-01 | |  110 |   0 |   0

The MNIST database of handwritten digits, available from this page, has a training set of 60,000 examples, and a test set of 10,000 examples. It is a subset of a larger set available from NIST. The digits have been size-normalized and centered in a fixed-size image.

It is a good database for people who want to try learning techniques and pattern recognition methods on real-world data while spending minimal efforts on preprocessing and formatting.


The original black and white (bilevel) images from NIST were size normalized to fit in a 20x20 pixel box while preserving their aspect ratio. The resulting images contain grey levels as a result of the anti-aliasing technique used by the normalization algorithm. the images were centered in a 28x28 image by computing the center of mass of the pixels, and translating the image so as to position this point at the center of the 28x28 field.

With some classification methods (particuarly template-based methods, such as SVM and K-nearest neighbors), the error rate improves when the digits are centered by bounding box rather than center of mass. If you do this kind of pre-processing, you should report it in your publications.

The MNIST database was constructed from NIST's Special Database 3 and Special Database 1 which contain binary images of handwritten digits. NIST originally designated SD-3 as their training set and SD-1 as their test set. However, SD-3 is much cleaner and easier to recognize than SD-1. The reason for this can be found on the fact that SD-3 was collected among Census Bureau employees, while SD-1 was collected among high-school students. Drawing sensible conclusions from learning experiments requires that the result be independent of the choice of training set and test among the complete set of samples. Therefore it was necessary to build a new database by mixing NIST's datasets.

The MNIST training set is composed of 30,000 patterns from SD-3 and 30,000 patterns from SD-1. Our test set was composed of 5,000 patterns from SD-3 and 5,000 patterns from SD-1. The 60,000 pattern training set contained examples from approximately 250 writers. We made sure that the sets of writers of the training set and test set were disjoint.

SD-1 contains 58,527 digit images written by 500 different writers. In contrast to SD-3, where blocks of data from each writer appeared in sequence, the data in SD-1 is scrambled. Writer identities for SD-1 is available and we used this information to unscramble the writers. We then split SD-1 in two: characters written by the first 250 writers went into our new training set. The remaining 250 writers were placed in our test set. Thus we had two sets with nearly 30,000 examples each. The new training set was completed with enough examples from SD-3, starting at pattern # 0, to make a full set of 60,000 training patterns. Similarly, the new test set was completed with SD-3 examples starting at pattern # 35,000 to make a full set with 60,000 test patterns. Only a subset of 10,000 test images (5,000 from SD-1 and 5,000 from SD-3) is available on this site. The full 60,000 sample training set is available.

Many methods have been tested with this training set and test set. Here are a few examples. Details about the methods are given in an upcoming paper. Some of those experiments used a version of the database where the input images where deskewed (by computing the principal axis of the shape that is closest to the vertical, and shifting the lines so as to make it vertical). In some other experiments, the training set was augmented with artificially distorted versions of the original training samples. The distortions are random combinations of shifts, scaling, skewing, and compression.
 

CLASSIFIERPREPROCESSINGTEST ERROR RATE (%)Reference
Linear Classifiers
linear classifier (1-layer NN)none12.0LeCun et al. 1998
linear classifier (1-layer NN)deskewing8.4LeCun et al. 1998
pairwise linear classifierdeskewing7.6LeCun et al. 1998
K-Nearest Neighbors
K-nearest-neighbors, Euclidean (L2)none5.0LeCun et al. 1998
K-nearest-neighbors, Euclidean (L2)none3.09Kenneth Wilder, U. Chicago
K-nearest-neighbors, L3none2.83Kenneth Wilder, U. Chicago
K-nearest-neighbors, Euclidean (L2)deskewing2.4LeCun et al. 1998
K-nearest-neighbors, Euclidean (L2)deskewing, noise removal, blurring1.80Kenneth Wilder, U. Chicago
K-nearest-neighbors, L3deskewing, noise removal, blurring1.73Kenneth Wilder, U. Chicago
K-nearest-neighbors, L3deskewing, noise removal, blurring, 1 pixel shift1.33Kenneth Wilder, U. Chicago
K-nearest-neighbors, L3deskewing, noise removal, blurring, 2 pixel shift1.22Kenneth Wilder, U. Chicago
K-NN with non-linear deformation (IDM)shiftable edges0.54Keysers et al. IEEE PAMI 2007
K-NN with non-linear deformation (P2DHMDM)shiftable edges0.52Keysers et al. IEEE PAMI 2007
K-NN, Tangent Distancesubsampling to 16x16 pixels1.1LeCun et al. 1998
K-NN, shape context matchingshape context feature extraction0.63Belongie et al. IEEE PAMI 2002
Boosted Stumps
boosted stumpsnone7.7Kegl et al., ICML 2009
products of boosted stumps (3 terms)none1.26Kegl et al., ICML 2009
boosted trees (17 leaves)none1.53Kegl et al., ICML 2009
stumps on Haar featuresHaar features1.02Kegl et al., ICML 2009
product of stumps on Haar f.Haar features0.87Kegl et al., ICML 2009
Non-Linear Classifiers
40 PCA + quadratic classifiernone3.3LeCun et al. 1998
1000 RBF + linear classifiernone3.6LeCun et al. 1998
SVMs
SVM, Gaussian Kernelnone1.4
SVM deg 4 polynomialdeskewing1.1LeCun et al. 1998
Reduced Set SVM deg 5 polynomialdeskewing1.0LeCun et al. 1998
Virtual SVM deg-9 poly [distortions]none0.8LeCun et al. 1998
Virtual SVM, deg-9 poly, 1-pixel jitterednone0.68DeCoste and Scholkopf, MLJ 2002
Virtual SVM, deg-9 poly, 1-pixel jittereddeskewing0.68DeCoste and Scholkopf, MLJ 2002
Virtual SVM, deg-9 poly, 2-pixel jittereddeskewing0.56DeCoste and Scholkopf, MLJ 2002
Neural Nets
2-layer NN, 300 hidden units, mean square errornone4.7LeCun et al. 1998
2-layer NN, 300 HU, MSE, [distortions]none3.6LeCun et al. 1998
2-layer NN, 300 HUdeskewing1.6LeCun et al. 1998
2-layer NN, 1000 hidden unitsnone4.5LeCun et al. 1998
2-layer NN, 1000 HU, [distortions]none3.8LeCun et al. 1998
3-layer NN, 300+100 hidden unitsnone3.05LeCun et al. 1998
3-layer NN, 300+100 HU [distortions]none2.5LeCun et al. 1998
3-layer NN, 500+150 hidden unitsnone2.95LeCun et al. 1998
3-layer NN, 500+150 HU [distortions]none2.45LeCun et al. 1998
3-layer NN, 500+300 HU, softmax, cross entropy, weight decaynone1.53Hinton, unpublished, 2005
2-layer NN, 800 HU, Cross-Entropy Lossnone1.6Simard et al., ICDAR 2003
2-layer NN, 800 HU, cross-entropy [affine distortions]none1.1Simard et al., ICDAR 2003
2-layer NN, 800 HU, MSE [elastic distortions]none0.9Simard et al., ICDAR 2003
2-layer NN, 800 HU, cross-entropy [elastic distortions]none0.7Simard et al., ICDAR 2003
NN, 784-500-500-2000-30 + nearest neighbor, RBM + NCA training [no distortions]none1.0Salakhutdinov and Hinton, AI-Stats 2007
6-layer NN 784-2500-2000-1500-1000-500-10 (on GPU) [elastic distortions]none0.35Ciresan et al. Neural Computation 10, 2010 and arXiv 1003.0358, 2010
committee of 25 NN 784-800-10 [elastic distortions]width normalization, deslanting0.39Meier et al. ICDAR 2011
deep convex net, unsup pre-training [no distortions]none0.83Deng et al. Interspeech 2010
Convolutional nets
Convolutional net LeNet-1subsampling to 16x16 pixels1.7LeCun et al. 1998
Convolutional net LeNet-4none1.1LeCun et al. 1998
Convolutional net LeNet-4 with K-NN instead of last layernone1.1LeCun et al. 1998
Convolutional net LeNet-4 with local learning instead of last layernone1.1LeCun et al. 1998
Convolutional net LeNet-5, [no distortions]none0.95LeCun et al. 1998
Convolutional net LeNet-5, [huge distortions]none0.85LeCun et al. 1998
Convolutional net LeNet-5, [distortions]none0.8LeCun et al. 1998
Convolutional net Boosted LeNet-4, [distortions]none0.7LeCun et al. 1998
Trainable feature extractor + SVMs [no distortions]none0.83Lauer et al., Pattern Recognition 40-6, 2007
Trainable feature extractor + SVMs [elastic distortions]none0.56Lauer et al., Pattern Recognition 40-6, 2007
Trainable feature extractor + SVMs [affine distortions]none0.54Lauer et al., Pattern Recognition 40-6, 2007
unsupervised sparse features + SVM, [no distortions]none0.59Labusch et al., IEEE TNN 2008
Convolutional net, cross-entropy [affine distortions]none0.6Simard et al., ICDAR 2003
Convolutional net, cross-entropy [elastic distortions]none0.4Simard et al., ICDAR 2003
large conv. net, random features [no distortions]none0.89Ranzato et al., CVPR 2007
large conv. net, unsup features [no distortions]none0.62Ranzato et al., CVPR 2007
large conv. net, unsup pretraining [no distortions]none0.60Ranzato et al., NIPS 2006
large conv. net, unsup pretraining [elastic distortions]none0.39Ranzato et al., NIPS 2006
large conv. net, unsup pretraining [no distortions]none0.53Jarrett et al., ICCV 2009
large/deep conv. net, 1-20-40-60-80-100-120-120-10 [elastic distortions]none0.35Ciresan et al. IJCAI 2011
committee of 7 conv. net, 1-20-P-40-P-150-10 [elastic distortions]width normalization0.27 +-0.02Ciresan et al. ICDAR 2011
committee of 35 conv. net, 1-20-P-40-P-150-10 [elastic distortions]width normalization0.23Ciresan et al. CVPR 2012



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