Jouni Järvinen

On the structure of rough approximations

We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximations of the elements of an atomic Boolean lattice are studied.

Lattice theory for rough sets

This work focuses on lattice-theoretical foundations of rough set theory. It consist of the following sections: 1: Introduction 2: Basic Notions and Notation, 3: Orders and Lattices, 4: Distributive, Boolean, and Stone Lattices, 5: Closure Systems and Topologies, 6: Fixpoints and Closure Operators on Ordered Sets, 7: Galois Connections and Their Fixpoints, 8: Information Systems, 9: Rough Set Approximations, and 10: Lattices of Rough Sets. At the end of each section, brief bibliographic remarks are presented.

Approximations and Rough Sets Based on Tolerances

In rough set theory it is supposed that the knowledge about objects is limited by an indiscernibility relation. Commonly indiscernibility relations are assumed to be equivalences interpreted so that two objects are equivalent if we cannot distinguish them by their properties. However, there are natural indiscernibility relations which are not transitive, and here we assume that the knowledge about objects is restricted by a tolerance relation R. We study R-approximations, R-definable sets, R-equalities, and investigate briefly the structure of R-rough sets.

An efficient algorithm for learning to rank from preference graphs

In this paper, we introduce a framework for regularized least-squares (RLS) type of ranking cost functions and we propose three such cost functions. Further, we propose a kernel-based preference learning algorithm, which we call RankRLS, for minimizing these functions. It is shown that RankRLS has many computational advantages compared to the ranking algorithms that are based on minimizing other types of costs, such as the hinge cost. In particular, we present efficient algorithms for training, parameter selection, multiple output learning, cross-validation, and large-scale learning. Circumstances under which these computational benefits make RankRLS preferable to RankSVM are considered. We evaluate RankRLS on four different types of ranking tasks using RankSVM and the standard RLS regression as the baselines. RankRLS outperforms the standard RLS regression and its performance is very similar to that of RankSVM, while RankRLS has several computational benefits over RankSVM.

Analysis of link grammar on biomedical dependency corpus targeted at protein-protein interactions

In this paper, we present an evaluation of the Link Grammar parser on a corpus consisting of sentences describing protein-protein interactions. We introduce the notion of an interaction subgraph, which is the subgraph of a dependency graph expressing a protein-protein interaction. We measure the performance of the parser for recovery of dependencies, fully correct linkages and interaction subgraphs. We analyze the causes of parser failure and report specific causes of error, and identify potential modifications to the grammar to address the identified issues. We also report and discuss the effect of an extension to the dictionary of the parser.

The Ordered Set of Rough Sets

We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the ordered sets of rough sets that are not necessarily lattices we present some possible canonical completions.

A unifying study between modal-like operators, topologies and fuzzy sets

The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is isomorphic to the categories of preordered sets and Alexandrov spaces. Moreover, joins, meets and complements for the objects in this category of representatives are determined. This suggests how to define for fuzzy subsets of a certain universe the lattice operations in a canonical way.

Evaluation of two dependency parsers on biomedical corpus targeted at protein-protein interactions.

We present an evaluation of Link Grammar and Connexor Machinese Syntax, two major broad-coverage dependency parsers, on a custom hand-annotated corpus consisting of sentences regarding protein-protein interactions. In the evaluation, we apply the notion of an interaction subgraph, which is the subgraph of a dependency graph expressing a protein-protein interaction. We measure the performance of the parsers for recovery of individual dependencies, fully correct parses, and interaction subgraphs. For Link Grammar, an open system that can be inspected in detail, we further perform a comprehensive failure analysis, report specific causes of error, and suggest potential modifications to the grammar. We find that both parsers perform worse on biomedical English than previously reported on general English. While Connexor Machinese Syntax significantly outperforms Link Grammar, the failure analysis suggests specific ways in which the latter could be modified for better performance in the domain.

Representation of Nelson algebras by rough sets determined by quasiorders

In this paper, we show that every quasiorder R induces a Nelson algebra