  In this work we define and analyze the bilinear models which replace the
conventional linear operation used in many building blocks of machine learning
(ML). The main idea is to devise the ML algorithms which are adapted to the
objects they treat. In the case of monochromatic images, we show that the
bilinear operation exploits better the structure of the image than the
conventional linear operation which ignores the spatial relationship between
the pixels. This translates into significantly smaller number of parameters
required to yield the same performance. We show numerical examples of
classification in the MNIST data set.
