Representing chord sequences in OWL

Chord symbols and progressions are a common way to describe musical harmony. In this paper we present SEQ, a pattern representation using the Web Ontology Language OWL DL and its application to modelling chord sequences. SEQ provides a logical representation of order information, which is not available directly in OWL DL, together with an intuitive notation. It therefore allows the use of OWL reasoners for tasks such as classification of sequences by patterns and determining subsumption relationships between the patterns. The SEQ representation is used to express distinctive pattern obtained using data mining of multiple viewpoints of chord sequences

Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Several admissible methods are constructed and two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Alternative clustering methodologies and axioms are further considered. Allowing the outcome of hierarchical clustering to be asymmetric, so that it matches the asymmetry of the original data, leads to the inception of quasi-clustering methods. The existence of a unique quasi-clustering method is shown. Allowing clustering in a two-node network to proceed at the minimum of the two dissimilarities generates an alternative axiomatic construction. There is a unique clustering method in this case too. The paper also develops algorithms for the computation of hierarchical clusters using matrix powers on a min-max dioid algebra and studies the stability of the methods proposed. We proved that most of the methods introduced in this paper are such that similar networks yield similar hierarchical clustering results. Algorithms are exemplified through their application to networks describing internal migration within states of the United States (U.S.) and the interrelation between sectors of the U.S. economy.Comment: This is a largely extended version of the previous conference submission under the same title. The current version contains the material in the previous version (published in ICASSP 2013) as well as material presented at the Asilomar Conference on Signal, Systems, and Computers 2013, GlobalSIP 2013, and ICML 2014. Also, unpublished material is included in the current versio

A formal theory for spatial representation and reasoning in biomedical ontologies

Objective: The objective of this paper is to demonstrate how a formal spatial theory can be used as an important tool for disambiguating the spatial information embodied in biomedical ontologies and for enhancing their automatic reasoning capabilities. Method and Materials: This paper presents a formal theory of parthood and location relations among individuals, called Basic Inclusion Theory (BIT). Since biomedical ontologies are comprised of assertions about classes of individuals (rather than assertions about individuals), we define parthood and location relations among classes in the extended theory BIT+Cl (Basic Inclusion Theory for Classes). We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise in two ontologies concerned with human anatomy: the Foundational Model of Anatomy (FMA) and GALEN. Results: We find that in both the FMA and GALEN, class-level spatial relations with different logical properties are not always explicitly distinguished. As a result, the spatial information included in these biomedical ontologies is often ambiguous and the possibilities for implementing consistent automatic reasoning within or across ontologies are limited. Conclusion: Precise formal characterizations of all spatial relations assumed by a biomedical ontology are necessary to ensure that the information embodied in the ontology can be fully and coherently utilized in a computational environment. This paper can be seen as an important beginning step toward achieving this goal, but much more work is along these lines is required

OntoMathPROOntoMath^{PRO} Ontology: A Linked Data Hub for Mathematics

In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic Web - 5th International Conferenc

More is not Always Better: The Negative Impact of A-box Materialization on RDF2vec Knowledge Graph Embeddings

RDF2vec is an embedding technique for representing knowledge graph entities in a continuous vector space. In this paper, we investigate the effect of materializing implicit A-box axioms induced by subproperties, as well as symmetric and transitive properties. While it might be a reasonable assumption that such a materialization before computing embeddings might lead to better embeddings, we conduct a set of experiments on DBpedia which demonstrate that the materialization actually has a negative effect on the performance of RDF2vec. In our analysis, we argue that despite the huge body of work devoted on completing missing information in knowledge graphs, such missing implicit information is actually a signal, not a defect, and we show examples illustrating that assumption.Comment: Accepted at the Workshop on Combining Symbolic and Sub-symbolic methods and their Applications (CSSA 2020

Exploring Causal Influences

Recent data mining techniques exploit patterns of statistical independence in multivariate data to make conjectures about cause/effect relationships. These relationships can be used to construct causal graphs, which are sometimes represented by weighted node-link diagrams, with nodes representing variables and combinations of weighted links and/or nodes showing the strength of causal relationships. We present an interactive visualization for causal graphs (ICGs), inspired in part by the Influence Explorer. The key principles of this visualization are as follows: Variables are represented with vertical bars attached to nodes in a graph. Direct manipulation of variables is achieved by sliding a variable value up and down, which reveals causality by producing instantaneous change in causally and/or probabilistically linked variables. This direct manipulation technique gives users the impression they are causally influencing the variables linked to the one they are manipulating. In this context, we demonstrate the subtle distinction between seeing and setting of variable values, and in an extended example, show how this visualization can help a user understand the relationships in a large variable set, and with some intuitions about the domain and a few basic concepts, quickly detect bugs in causal models constructed from these data mining techniques

Ontology reasoning using SPARQL query: A case study of e-learning usage

The involvement of learning pedagogy towards implementation of e-learning contribute to the additional values, and it is assign as a benchmark when the investigation and evaluation will carry out. The results obtained later believed would be fit to the domain problem.The results might provide instructional theories including recommendation after reasoning that can be used to improve the quality of teaching and learning in the virtual classroom. Ontology as formal conceptualization has been chosen as research methodology. Ontology conceptualization helps to illustrate the e-learning usage including activities and actions, likewise learning pedagogy in the form of concepts, class, relationships and instances. The ontology constructed in this paper is used in conjunction with the SPARQL rules, which are designed to test the reasoning ability of ontology. Reasoning results should be able to describe the knowledge contained in ontology, as well the facts on it. The SPARQL rules contains triplets to verify if the students are actively engaged in a meaningful way towards e-learning usage. The backward engine is optimized to store the facts obtained from queries. Development of ontology knowledge based and reasoning rules with SPARQL queries allow to contribute a sustainable competitive advantages regarding the e-learning utilization. Eventually, this research produced a learning ontology with reasoning capability to get meaningful information