MNIST

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The MNIST database, an extension of the NIST database, is a low-complexity data collection of handwritten digits used to train and test various supervised machine learning algorithms. The database contains 70,000 28x28 black and white images representing the digits zero through nine. The data is split into two subsets, with 60,000 images belonging to the training set and 10,000 images belonging to the testing set. The separation of images ensures that given what an adequately trained model has learned previously, it can accurately classify relevant images not previously examined.

As it can be seen from the image above, the handwritten digits consist of varying styles and complexities. For example, in the first column, there are three 3s with distinct defining characteristics. These digits further differ from the 3s that exist in column five. The variety in the dataset gives robustness to an appropriately trained model, which is evident through the accuracy on the testing data (up to 99.65%) when fed through such model.

Purpose of Database and its Applications

In simple terms, MNIST can be thought of as the “Hello, World!” of machine learning. MNIST is primarily used to experiment with different machine learning algorithms and to compare their relative strengths. Yann LeCun, one of the three researchers behind the creation of MNIST, has devoted a portion of his research to using MNIST to experiment with cutting edge algorithms, which can be seen on his personal website yann.lecun.com. Many researchers, hobbyists, and students alike continue to use MNIST alongside their algorithmic implementations and other popular datasets as a way to solidify their understanding of the fundamental concepts in machine learning and to compare their new algorithms against existing cutting edge research.

MNIST Dataset File Formats

The data is stored in a very simple file format designed for storing vectors and multidimensional matrices. General info on this format is given at the end of this page, but you don't need to read that to use the data files.

All the integers in the files are stored in the MSB first (high endian) format used by most non-Intel processors. Users of Intel processors and other low-endian machines must flip the bytes of the header.

There are 4 files:

train-images-idx3-ubyte: training set images
train-labels-idx1-ubyte: training set labels
t10k-images-idx3-ubyte: test set images
t10k-labels-idx1-ubyte: test set labels

The training set contains 60000 examples, and the test set 10000 examples.

The first 5000 examples of the test set are taken from the original NIST training set. The last 5000 are taken from the original NIST test set. The first 5000 are cleaner and easier than the last 5000.

TRAINING SET LABEL FILE (train-labels-idx1-ubyte):

[offset] [type]          [value]          [description]
0000     32 bit integer 0x00000801(2049) magic number (MSB first)
0004     32 bit integer 60000            number of items
0008     unsigned byte   ??               label
0009     unsigned byte   ??               label
........
xxxx     unsigned byte   ??               label

The labels values are 0 to 9.

TRAINING SET IMAGE FILE (train-images-idx3-ubyte):

[offset] [type]          [value]          [description]
0000     32 bit integer 0x00000803(2051) magic number
0004     32 bit integer 60000            number of images
0008     32 bit integer 28               number of rows
0012     32 bit integer 28               number of columns
0016     unsigned byte   ??               pixel
0017     unsigned byte   ??               pixel
........
xxxx     unsigned byte   ??               pixel

Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).

TEST SET LABEL FILE (t10k-labels-idx1-ubyte):

[offset] [type]          [value]          [description]
0000     32 bit integer 0x00000801(2049) magic number (MSB first)
0004     32 bit integer 10000            number of items
0008     unsigned byte   ??               label
0009     unsigned byte   ??               label
........
xxxx     unsigned byte   ??               label

The labels values are 0 to 9.

TEST SET IMAGE FILE (t10k-images-idx3-ubyte):

[offset] [type]          [value]          [description]
0000     32 bit integer 0x00000803(2051) magic number
0004     32 bit integer 10000            number of images
0008     32 bit integer 28               number of rows
0012     32 bit integer 28               number of columns
0016     unsigned byte   ??               pixel
0017     unsigned byte   ??               pixel
........
xxxx     unsigned byte   ??               pixel

Pixels are organized row-wise. Pixel values are 0 to 255. 0 means background (white), 255 means foreground (black).

THE IDX FILE FORMAT

the IDX file format is a simple format for vectors and multidimensional matrices of various numerical types.

The basic format is

magic number
size in dimension 0
size in dimension 1
size in dimension 2
.....
size in dimension N
data

The magic number is an integer (MSB first). The first 2 bytes are always 0.

The third byte codes the type of the data:
0x08: unsigned byte
0x09: signed byte
0x0B: short (2 bytes)
0x0C: int (4 bytes)
0x0D: float (4 bytes)
0x0E: double (8 bytes)

The 4-th byte codes the number of dimensions of the vector/matrix: 1 for vectors, 2 for matrices....

The sizes in each dimension are 4-byte integers (MSB first, high endian, like in most non-Intel processors).

The data is stored like in a C array, i.e. the index in the last dimension changes the fastest.