  We suggest a novel classification algorithm that is based on local
approximations and explain its connections with Artificial Neural Networks
(ANNs) and Nearest Neighbour classifiers. We illustrate it on the datasets
MNIST and EMNIST of images of handwritten digits. We use the dataset MNIST to
find parameters of our algorithm and apply it with these parameters to the
challenging EMNIST dataset. It is demonstrated that the algorithm misclassifies
0.42% of the images of EMNIST and therefore significantly outperforms
predictions by humans and shallow artificial neural networks (ANNs with few
hidden layers) that both have more than 1.3% of errors
