mnist_784

**Author**: Yann LeCun, Corinna Cortes, Christopher J.C. Burges
**Source**: [MNIST Website](http://yann.lecun.com/exdb/mnist/) - Date unknown
**Please cite**:

The MNIST database of handwritten digits with 784 features, raw data available at: http://yann.lecun.com/exdb/mnist/. It can be split in a training set of the first 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 (particularly 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 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.

**作者**：扬·勒丘恩（Yann LeCun）、科琳娜·科特斯（Corinna Cortes）、克里斯托弗·J·C·伯吉斯（Christopher J.C. Burges）
**来源**：[MNIST官方网站](http://yann.lecun.com/exdb/mnist/) —— 日期不详
**请引用如下**：

MNIST（Modified National Institute of Standards and Technology）数据库包含784维特征的手写数字数据集，原始数据可从http://yann.lecun.com/exdb/mnist/ 获取。该数据集可划分为包含前60000个样本的训练集，以及包含10000个样本的测试集。

它是美国国家标准与技术研究院（National Institute of Standards and Technology, NIST）更大规模数据集的一个子集。所有数字均经过尺寸标准化处理，并在固定尺寸图像中居中对齐。对于希望在真实世界数据上尝试学习算法与模式识别方法，且希望尽可能减少预处理与格式调整工作量的研究者而言，这是一个非常理想的测试数据库。NIST提供的原始黑白二值图像经尺寸标准化后，被适配至20×20像素的方框中，同时保留了原始的长宽比。由于标准化算法使用了抗锯齿（anti-aliasing）技术，最终生成的图像包含灰度层级。随后通过计算像素的质心，将图像平移至28×28图像的中心位置，从而完成居中对齐。

部分分类方法（尤其是基于模板的方法，如支持向量机（Support Vector Machine, SVM）和K近邻（K-nearest neighbors, KNN））在使用边界框而非质心进行数字居中预处理时，错误率会有所降低。若采用此类预处理方式，请在您的出版物中予以说明。MNIST数据集的构建源自NIST的原始数据集：NIST最初将SD-3作为训练集，SD-1作为测试集。但SD-3相比SD-1更为清晰，更易于识别。究其原因，SD-3的样本采集自美国人口普查局员工，而SD-1的样本则采集自高中生。从机器学习实验中得出可靠结论，要求实验结果不受训练集与测试集的样本选取方式影响。因此有必要通过混合NIST的两个数据集来构建新的数据库。

MNIST的训练集由来自SD-3的30000个样本和来自SD-1的30000个样本组成。我们的测试集则由来自SD-3的5000个样本和来自SD-1的5000个样本组成。这一60000个样本的训练集涵盖了约250名书写者的样本。我们确保了训练集与测试集的书写者群体完全无重叠。SD-1包含58527张由500名不同书写者书写的数字图像。与SD-3中每位书写者的样本按顺序排列不同，SD-1的数据是打乱的。SD-1的书写者身份信息可公开获取，我们利用该信息对数据按书写者进行了重新分组整理。随后我们将SD-1划分为两部分：前250名书写者的样本被纳入新的训练集，剩余250名书写者的样本则被纳入测试集。由此我们得到了两个各接近30000个样本的数据集。新的训练集通过从SD-3的第0号样本开始补充足够的样本，最终组成完整的60000个训练样本。同理，新的测试集通过从SD-3的第35000号样本开始补充样本，最终组成完整的60000个测试样本。本网站仅提供了10000张测试图像的子集（其中5000张来自SD-1，5000张来自SD-3），完整的60000个训练样本数据集可供获取。