  Representation learning is currently a very hot topic in modern machine
learning, mostly due to the great success of the deep learning methods. In
particular low-dimensional representation which discriminates classes can not
only enhance the classification procedure, but also make it faster, while
contrary to the high-dimensional embeddings can be efficiently used for visual
based exploratory data analysis.
  In this paper we propose Maximum Entropy Linear Manifold (MELM), a
multidimensional generalization of Multithreshold Entropy Linear Classifier
model which is able to find a low-dimensional linear data projection maximizing
discriminativeness of projected classes. As a result we obtain a linear
embedding which can be used for classification, class aware dimensionality
reduction and data visualization. MELM provides highly discriminative 2D
projections of the data which can be used as a method for constructing robust
classifiers.
  We provide both empirical evaluation as well as some interesting theoretical
properties of our objective function such us scale and affine transformation
invariance, connections with PCA and bounding of the expected balanced accuracy
error.
