Vector Measure

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Ted Pedersen - One of the best experts on this subject based on the ideXlab platform.

  • duluth measuring degrees of relational similarity with the gloss Vector Measure of semantic relatedness
    Joint Conference on Lexical and Computational Semantics, 2012
    Co-Authors: Ted Pedersen
    Abstract:

    This paper describes the Duluth systems that participated in Task 2 of SemEval-2012. These systems were unsupervised and relied on variations of the Gloss Vector Measure found in the freely available software package WordNet:: Similarity. This method was moderately successful for the Class-Inclusion, Similar, Contrast, and Non-Attribute categories of semantic relations, but mimicked a random baseline for the other six categories.

  • semantic relatedness study using second order co occurrence Vectors computed from biomedical corpora umls and wordnet
    International Health Informatics Symposium, 2012
    Co-Authors: Ying Liu, Ted Pedersen, Bridget T Mcinnes, Genevieve Meltonmeaux, Serguei V S Pakhomov
    Abstract:

    Automated Measures of semantic relatedness are important for effectively processing medical data for a variety of tasks such as information retrieval and natural language processing. In this paper, we present a context Vector approach that can compute the semantic relatedness between any pair of concepts in the Unified Medical Language System (UMLS). Our approach has been developed on a corpus of inpatient clinical reports. We use 430 pairs of clinical concepts manually rated for semantic relatedness as the reference standard. The experiments demonstrate that incorporating a combination of the UMLS and WordNet definitions can improve the semantic relatedness. The paper also shows that second order co-occurrence Vector Measure is a more effective approach than path-based methods for semantic relatedness.

  • Measures of semantic similarity and relatedness in the biomedical domain
    Journal of Biomedical Informatics, 2007
    Co-Authors: Ted Pedersen, Serguei V S Pakhomov, Siddharth Patwardhan, Christopher G Chute
    Abstract:

    Measures of semantic similarity between concepts are widely used in Natural Language Processing. In this article, we show how six existing domain-independent Measures can be adapted to the biomedical domain. These Measures were originally based on WordNet, an English lexical database of concepts and relations. In this research, we adapt these Measures to the SNOMED-CT^(R) ontology of medical concepts. The Measures include two path-based Measures, and three Measures that augment path-based Measures with information content statistics from corpora. We also derive a context Vector Measure based on medical corpora that can be used as a Measure of semantic relatedness. These six Measures are evaluated against a newly created test bed of 30 medical concept pairs scored by three physicians and nine medical coders. We find that the medical coders and physicians differ in their ratings, and that the context Vector Measure correlates most closely with the physicians, while the path-based Measures and one of the information content Measures correlates most closely with the medical coders. We conclude that there is a role both for more flexible Measures of relatedness based on information derived from corpora, as well as for Measures that rely on existing ontological structures.

Arno B J Kuijlaars - One of the best experts on this subject based on the ideXlab platform.

  • orthogonal polynomials in the normal matrix model with a cubic potential
    Advances in Mathematics, 2012
    Co-Authors: Pavel Bleher, Arno B J Kuijlaars
    Abstract:

    Abstract We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to regularize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential weight on the cut-off region on the complex plane. In the present paper we show how to define orthogonal polynomials on a specially chosen system of infinite contours on the complex plane, without any cut-off, which satisfy the same recurrence algebraic identity that is asymptotically valid for the orthogonal polynomials of Elbau and Felder. The main goal of this paper is to develop the Riemann–Hilbert (RH) approach to the orthogonal polynomials under consideration and to obtain their asymptotic behavior on the complex plane as the degree n of the polynomial goes to infinity. As the first step in the RH approach, we introduce an auxiliary Vector equilibrium problem for a pair of Measures ( μ 1 , μ 2 ) on the complex plane. We then formulate a 3×3 matrix valued RH problem for the orthogonal polynomials in hand, and we apply the nonlinear steepest descent method of Deift–Zhou to the asymptotic analysis of the RH problem. The central steps in our study are a sequence of transformations of the RH problem, based on the equilibrium Vector Measure ( μ 1 , μ 2 ) , and the construction of a global parametrix. The main result of this paper is a derivation of the large n asymptotics of the orthogonal polynomials on the whole complex plane. We prove that the distribution of zeros of the orthogonal polynomials converges to the Measure μ 1 , the first component of the equilibrium Measure. We also obtain analytical results for the Measure μ 1 relating it to the distribution of eigenvalues in the normal matrix model which is uniform in a domain bounded by a simple closed curve.

  • orthogonal polynomials in the normal matrix model with a cubic potential
    arXiv: Mathematical Physics, 2011
    Co-Authors: Pavel Bleher, Arno B J Kuijlaars
    Abstract:

    We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to reguralize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential weight on the cut-off region on the complex plane. In the present paper we show how to define orthogonal polynomials on a specially chosen system of infinite contours on the complex plane, without any cut-off, which satisfy the same recurrence algebraic identity that is asymptotically valid for the orthogonal polynomials of Elbau and Felder. The main goal of this paper is to develop the Riemann-Hilbert (RH) approach to the orthogonal polynomials under consideration and to obtain their asymptotic behavior on the complex plane as the degree $n$ of the polynomial goes to infinity. As the first step in the RH approach, we introduce an auxiliary Vector equilibrium problem for a pair of Measures $(\mu_1,\mu_2)$ on the complex plane. We then formulate a $3\times 3$ matrix valued RH problem for the orthogonal polynomials in hand, and we apply the nonlinear steepest descent method of Deift-Zhou to the asymptotic analysis of the RH problem. The central steps in our study are a sequence of transformations of the RH problem, based on the equilibrium Vector Measure $(\mu_1,\mu_2)$, and the construction of a global parametrix. The main result of this paper is a derivation of the large $n$ asymptotics of the orthogonal polynomials on the whole complex plane. We prove that the distribution of zeros of the orthogonal polynomials converges to the Measure $\mu_1$, the first component of the equilibrium Measure. We also obtain analytical results for the Measure $\mu_1$ relating it to the distribution of eigenvalues in the normal matrix model which is uniform in a domain bounded by a simple closed curve.

Stan Matwin - One of the best experts on this subject based on the ideXlab platform.

  • simdef definition based semantic similarity Measure of gene ontology terms for functional similarity analysis of genes
    Bioinformatics, 2016
    Co-Authors: Ahmad Pesaranghader, Stan Matwin, Marina Sokolova, Robert G Beiko
    Abstract:

    Measures of protein functional similarity are essential tools for function prediction, evaluation of protein-protein interactions (PPIs) and other applications. Several existing methods perform comparisons between proteins based on the semantic similarity of their GO terms; however, these Measures are highly sensitive to modifications in the topological structure of GO, tend to be focused on specific analytical tasks and concentrate on the GO terms themselves rather than considering their textual definitions.We introduce simDEF, an efficient method for measuring semantic similarity of GO terms using their GO definitions, which is based on the Gloss Vector Measure commonly used in natural language processing. The simDEF approach builds optimized definition Vectors for all relevant GO terms, and expresses the similarity of a pair of proteins as the cosine of the angle between their definition Vectors. Relative to existing similarity Measures, when validated on a yeast reference database, simDEF improves correlation with sequence homology by up to 50%, shows a correlation improvement >4% with gene expression in the biological process hierarchy of GO and increases PPI predictability by > 2.5% in F1 score for molecular function hierarchy.Datasets, results and source code are available at http://kiwi.cs.dal.ca/Software/simDEF CONTACT: ahmad.pgh@dal.ca or beiko@cs.dal.caSupplementary data are available at Bioinformatics online.

  • simdef definition based semantic similarity Measure of gene ontology terms for functional similarity analysis of genes
    Bioinformatics, 2016
    Co-Authors: Ahmad Pesaranghader, Stan Matwin, Marina Sokolova, Robert G Beiko
    Abstract:

    MOTIVATION Measures of protein functional similarity are essential tools for function prediction, evaluation of protein-protein interactions (PPIs) and other applications. Several existing methods perform comparisons between proteins based on the semantic similarity of their GO terms; however, these Measures are highly sensitive to modifications in the topological structure of GO, tend to be focused on specific analytical tasks and concentrate on the GO terms themselves rather than considering their textual definitions. RESULTS We introduce simDEF, an efficient method for measuring semantic similarity of GO terms using their GO definitions, which is based on the Gloss Vector Measure commonly used in natural language processing. The simDEF approach builds optimized definition Vectors for all relevant GO terms, and expresses the similarity of a pair of proteins as the cosine of the angle between their definition Vectors. Relative to existing similarity Measures, when validated on a yeast reference database, simDEF improves correlation with sequence homology by up to 50%, shows a correlation improvement >4% with gene expression in the biological process hierarchy of GO and increases PPI predictability by > 2.5% in F1 score for molecular function hierarchy. AVAILABILITY AND IMPLEMENTATION Datasets, results and source code are available at http://kiwi.cs.dal.ca/Software/simDEF CONTACT: ahmad.pgh@dal.ca or beiko@cs.dal.ca SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Ahmad Pesaranghader - One of the best experts on this subject based on the ideXlab platform.

  • simdef definition based semantic similarity Measure of gene ontology terms for functional similarity analysis of genes
    Bioinformatics, 2016
    Co-Authors: Ahmad Pesaranghader, Stan Matwin, Marina Sokolova, Robert G Beiko
    Abstract:

    Measures of protein functional similarity are essential tools for function prediction, evaluation of protein-protein interactions (PPIs) and other applications. Several existing methods perform comparisons between proteins based on the semantic similarity of their GO terms; however, these Measures are highly sensitive to modifications in the topological structure of GO, tend to be focused on specific analytical tasks and concentrate on the GO terms themselves rather than considering their textual definitions.We introduce simDEF, an efficient method for measuring semantic similarity of GO terms using their GO definitions, which is based on the Gloss Vector Measure commonly used in natural language processing. The simDEF approach builds optimized definition Vectors for all relevant GO terms, and expresses the similarity of a pair of proteins as the cosine of the angle between their definition Vectors. Relative to existing similarity Measures, when validated on a yeast reference database, simDEF improves correlation with sequence homology by up to 50%, shows a correlation improvement >4% with gene expression in the biological process hierarchy of GO and increases PPI predictability by > 2.5% in F1 score for molecular function hierarchy.Datasets, results and source code are available at http://kiwi.cs.dal.ca/Software/simDEF CONTACT: ahmad.pgh@dal.ca or beiko@cs.dal.caSupplementary data are available at Bioinformatics online.

  • simdef definition based semantic similarity Measure of gene ontology terms for functional similarity analysis of genes
    Bioinformatics, 2016
    Co-Authors: Ahmad Pesaranghader, Stan Matwin, Marina Sokolova, Robert G Beiko
    Abstract:

    MOTIVATION Measures of protein functional similarity are essential tools for function prediction, evaluation of protein-protein interactions (PPIs) and other applications. Several existing methods perform comparisons between proteins based on the semantic similarity of their GO terms; however, these Measures are highly sensitive to modifications in the topological structure of GO, tend to be focused on specific analytical tasks and concentrate on the GO terms themselves rather than considering their textual definitions. RESULTS We introduce simDEF, an efficient method for measuring semantic similarity of GO terms using their GO definitions, which is based on the Gloss Vector Measure commonly used in natural language processing. The simDEF approach builds optimized definition Vectors for all relevant GO terms, and expresses the similarity of a pair of proteins as the cosine of the angle between their definition Vectors. Relative to existing similarity Measures, when validated on a yeast reference database, simDEF improves correlation with sequence homology by up to 50%, shows a correlation improvement >4% with gene expression in the biological process hierarchy of GO and increases PPI predictability by > 2.5% in F1 score for molecular function hierarchy. AVAILABILITY AND IMPLEMENTATION Datasets, results and source code are available at http://kiwi.cs.dal.ca/Software/simDEF CONTACT: ahmad.pgh@dal.ca or beiko@cs.dal.ca SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Pavel Bleher - One of the best experts on this subject based on the ideXlab platform.

  • orthogonal polynomials in the normal matrix model with a cubic potential
    Advances in Mathematics, 2012
    Co-Authors: Pavel Bleher, Arno B J Kuijlaars
    Abstract:

    Abstract We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to regularize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential weight on the cut-off region on the complex plane. In the present paper we show how to define orthogonal polynomials on a specially chosen system of infinite contours on the complex plane, without any cut-off, which satisfy the same recurrence algebraic identity that is asymptotically valid for the orthogonal polynomials of Elbau and Felder. The main goal of this paper is to develop the Riemann–Hilbert (RH) approach to the orthogonal polynomials under consideration and to obtain their asymptotic behavior on the complex plane as the degree n of the polynomial goes to infinity. As the first step in the RH approach, we introduce an auxiliary Vector equilibrium problem for a pair of Measures ( μ 1 , μ 2 ) on the complex plane. We then formulate a 3×3 matrix valued RH problem for the orthogonal polynomials in hand, and we apply the nonlinear steepest descent method of Deift–Zhou to the asymptotic analysis of the RH problem. The central steps in our study are a sequence of transformations of the RH problem, based on the equilibrium Vector Measure ( μ 1 , μ 2 ) , and the construction of a global parametrix. The main result of this paper is a derivation of the large n asymptotics of the orthogonal polynomials on the whole complex plane. We prove that the distribution of zeros of the orthogonal polynomials converges to the Measure μ 1 , the first component of the equilibrium Measure. We also obtain analytical results for the Measure μ 1 relating it to the distribution of eigenvalues in the normal matrix model which is uniform in a domain bounded by a simple closed curve.

  • orthogonal polynomials in the normal matrix model with a cubic potential
    arXiv: Mathematical Physics, 2011
    Co-Authors: Pavel Bleher, Arno B J Kuijlaars
    Abstract:

    We consider the normal matrix model with a cubic potential. The model is ill-defined, and in order to reguralize it, Elbau and Felder introduced a model with a cut-off and corresponding system of orthogonal polynomials with respect to a varying exponential weight on the cut-off region on the complex plane. In the present paper we show how to define orthogonal polynomials on a specially chosen system of infinite contours on the complex plane, without any cut-off, which satisfy the same recurrence algebraic identity that is asymptotically valid for the orthogonal polynomials of Elbau and Felder. The main goal of this paper is to develop the Riemann-Hilbert (RH) approach to the orthogonal polynomials under consideration and to obtain their asymptotic behavior on the complex plane as the degree $n$ of the polynomial goes to infinity. As the first step in the RH approach, we introduce an auxiliary Vector equilibrium problem for a pair of Measures $(\mu_1,\mu_2)$ on the complex plane. We then formulate a $3\times 3$ matrix valued RH problem for the orthogonal polynomials in hand, and we apply the nonlinear steepest descent method of Deift-Zhou to the asymptotic analysis of the RH problem. The central steps in our study are a sequence of transformations of the RH problem, based on the equilibrium Vector Measure $(\mu_1,\mu_2)$, and the construction of a global parametrix. The main result of this paper is a derivation of the large $n$ asymptotics of the orthogonal polynomials on the whole complex plane. We prove that the distribution of zeros of the orthogonal polynomials converges to the Measure $\mu_1$, the first component of the equilibrium Measure. We also obtain analytical results for the Measure $\mu_1$ relating it to the distribution of eigenvalues in the normal matrix model which is uniform in a domain bounded by a simple closed curve.