Networks of Compound Object Comparators  Lukasz Sosnowski Systems Research Institute, Polish Academy of Sciences ul. Newelska 6, 01-447 Warsaw, Poland and Dituel Sp. z o.o. ul. Ostrobramska 101 lok. 206, 04-041 Warsaw, Poland l.sosnowski@dituel.pl Dominik ´ Sl¸ ezak Institute of Mathematics, University of Warsaw ul. Banacha 2, 02-097 Warsaw, Poland and Infobright Inc. ul. Krzywickiego 34 lok. 219, 02-078 Warsaw, Poland slezak@infobright.com Abstract —We discuss the theoretical background and some practical implementations of multilayered net- works of units, which compare compound objects for the purposes of their identification, matching and pars- ing. We show how our approach arises from the previous research on fuzzy comparators. We also show in what sense the flow of information in the considered networks follows the principles of rough mereology. Finally, we present some case studies of utilization of networks of comparators in the image and text processing. Index Terms—Compound Objects, Fuzzy Compara- tors, Networks of Comparators, Rough Mereology I. Introduction In our research so far, we proved that comparators of compound objects could be a useful tool for the tasks of identification and classification [1], [2]. In this article, we extend our methodology toward a framework for compara- tor networks, increasing a range of available techniques aimed at solving decision problems related to compound objects. In order to do this, we attempt to follow some paradigms of hierarchical learning and modeling [3], [4], as well as some mathematical models useful for dealing with relationships between object components [5], [6]. The article is organized as follows. Section II presents the background for our research. Sections III and IV outline the previous studies on comparators. Sections V and VI introduce the networks of comparators. Sections VII and VIII bring some case studies and conclusions. II. Preliminaries In our approach, the structures of compound objects and the corresponding comparator networks are formu- lated by utilizing ontologies. We follow [7] (see also [8]), where ontology is defined as a system specifying the structure of concepts reflecting representations of groups of objects with some common characteristics, various types of taxonomic and non-taxonomic relationships between Supported by the grant SP/I/1/77065/10 in frame of the strategic scientific research and experimental development program: “Inter- disciplinary System for Interactive Scientific and Scientific-Technical Information” founded by Polish National Centre for Research and Development (NCBiR), as well as grants 2011/01/B/ST6/03867 and 2012/05/B/ST6/03215 from Polish National Science Centre (NCN). concepts, as well as axioms and lexicons defining how to understand concepts and relations between them. An object is any element of the real world having its representation capable of being expressed by the adopted ontology. The following properties arise from ontological representation of objects: 1) An object always belongs to a certain class in the ontology. An object may belong to several classes. 2) An object has a property within a class. Features may vary by class. 3) The object may be in relation to other objects in the same ontology. We distinguish between compound and simple objects. Simple objects are atomic, standard entities that have cer- tain characteristics, but are not composed of other objects. Compound objects may consist of other objects, either simple or compound, according to their structure defined in the ontology. Their specification includes relations and connections between their sub-objects. Compound objects satisfy the following additional properties: 1) We can extract from them a minimum of two objects that can be independent entities. 2) Component sub-objects are interrelated by using ontological relationships. We will also refer to the notion of an information granule – a clump of objects drawn together on the basis of indis- tinguishability, similarity, or functionality [9], [10]. In our case, granules will be constructed as data representations of objects and their closest surroundings. Finally, we will use some notions from the mereology theory, where the basic idea is the relation of being a part [11]. We will follow the principles of rough mereology [3], which deals with questions of the form to what degree X is part of Y, using rough inclusion μ(X, Y ). As a result of an ontology-based decomposition of com- pound objects onto sub-objects we can reach a level of complexity, which begins to be easy enough to adjust a measure of similarity. By using rough mereology, we can then determine degrees of similarity between more compound objects by combining degrees of relationships between their simpler components.