This paper presents and evaluates two linear feature extractors based on mutual information. These feature extractors consider general dependencies between features and class labels, as opposed to well known linear methods such as PCA which does not consider class labels and LDA, which uses only simple low order dependencies. As evidenced by several simulations on high dimensional data sets, th...

In the paper we examine data dependencies in the algorithm of back substitution in the problem of solving triangular systems of linear equations. The aim of the paper is to illustrate the structural blanks (SB) notation in consistency proof of data dependencies in loop programs. Data dependency semantics of programs is introduced and investigated. The introduced notation constitutes the theoret...

This paper studies dependencies between random variables by means of information theoretic functionals such as the entropy and the mutual information. In particular, extremal dependencies (defined in terms of these functionals) are shown to have combinatorial structures corresponding to linear matroids. From a combinatorial point of view, this provides a characterization of a new class of matro...

Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness result does not rely ...

Dependencies play an important role in database theory. We study order dependencies (ODs)—and unidirectional order dependencies (UODs), sub-class of ODs—which describe the relationships among lexicographical orderings of sets of tuples. We investigate the inference problem for order dependencies. We establish the following: (i) a sound and complete chase procedure for ODs for testing logical im...