Use the N-tuple Classifier to classify handwritten images of numbers (0-9) using the MNIST handwritten digit data. The program will train the classifier using the training data, test the performance using the test data, and then summarize performance with a confusion matrix and will print out the accuracy.

To run, you will need to install the numpy and numba packages. This is for performance.

You'll also need the MNIST data, a copy of which I've checked into this repository.

The main program is mnist_ntuple.py

$ python3 mnist_ntuple.py data/train-images-idx3-ubyte data/train-labels-idx1-ubyte data/t10k-images-idx3-ubyte data/t10k-labels-idx1-ubyte 

The N-tuple classifier is pretty neat. It's relatively simple, potentially quite fast, and even with a naive implementation has an accuracy of around 91% on the MNIST data. But it isn't very popular, and is not typically discussed in introductory data science material.

The N-tuple classifier works by using subclassifiers (called modules). When training: each module will sample a small number of pixel positions from each image, determining which of the pixels are "active" (have a value above a threshold). A table is used to keep track of the number of times each label was encountered for the active sampled pixels.

When classifying an image: for each module, we sample the same pixel positions, and we sum up the number of times we've seen each label given the active sample pixels. The label with the highest count will be the label we choose.

For more information on n-tuple classifiers:

• Bledsoe and Browning. Pattern recognition and reading by machine. - The original paper
• http://www.theparticle.com/cs/bc/dsci/ntuple.pdf - Which this python implementation is based on
• https://haralick.org/ML/ntuple_classifier_10_2_2020.pdf

USAGE:

$ python3 mnist_ntuple.py -h
usage: mnist_ntuple.py [-h] train_images_file train_labels_file test_images_file test_labels_file
positional arguments:
 train_images_file file with the training data
 train_labels_file file with the training labels
 test_images_file file with the testing data
 test_labels_file file with the testing labels
optional arguments:
 -h, --help show this help message and exit

Here's an example run:

$ python3 mnist_ntuple.py data/train-images-idx3-ubyte data/train-labels-idx1-ubyte data/t10k-images-idx3-ubyte data/t10k-labels-idx1-ubyte 
Confusion Matrix:
 0 1 2 3 4 5 6 7 8 9
 0 920 0 6 3 0 41 6 0 3 1
 1 0 1080 4 7 1 14 2 1 24 2
 2 7 3 894 28 10 15 10 12 46 7
 3 0 0 5 921 1 47 0 8 15 13
 4 1 0 7 0 844 6 4 1 13 106
 5 2 2 1 31 4 822 3 2 10 15
 6 8 2 10 0 19 63 845 3 7 1
 7 0 2 22 5 2 1 0 916 19 61
 8 0 0 5 30 5 34 0 3 873 24
 9 4 2 4 15 12 5 1 8 13 945
accuracy: 0.9060