Multithreshold Entropy Linear Classifier (MELC) is a recent classifier idea which employs information theoretic concept in order to create a multithreshold maximum margin model. In this paper we analyze its consistency over multithreshold linear mode
ls and show that its objective function upper bounds the amount of misclassified points in a similar manner like hinge loss does in support vector machines. For further confirmation we also conduct some numerical experiments on five datasets.
Multithreshold Entropy Linear Classifier (MELC) is a density based model which searches for a linear projection maximizing the Cauchy-Schwarz Divergence of dataset kernel density estimation. Despite its good empirical results, one of its drawbacks is
the optimization speed. In this paper we analyze how one can speed it up through solving an approximate problem. We analyze two methods, both similar to the approximate solutions of the Kernel Density Estimation querying and provide adaptive schemes for selecting a crucial parameters based on user-specified acceptable error. Furthermore we show how one can exploit well known conjugate gradients and L-BFGS optimizers despite the fact that the original optimization problem should be solved on the sphere. All above methods and modifications are tested on 10 real life datasets from UCI repository to confirm their practical usability.
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 classifi
cation 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.
