The Experts below are selected from a list of 51 Experts worldwide ranked by ideXlab platform

Steyer Rolf - One of the best experts on this subject based on the ideXlab platform.

Hoffmann Irene - One of the best experts on this subject based on the ideXlab platform.

  • Linear discriminant analysis for high dimensional data : a comparison of sparse classification methods
    2014
    Co-Authors: Hoffmann Irene
    Abstract:

    Zsfassung in dt. Sprache. - Literaturverz. S. 61 - 62Die lineare Diskriminanzanalyse ist eine beliebte und weitverbreitete Methode des überwachten Lernens. In dieser Arbeit wird detailliert auf zwei lineare Klassifikationsmethoden eingegangen, die zu äquivalenten Modellen führen. Dies sind Fishers LDA und der optimal scoring Ansatz, die jeweils durch ein Optimierungsproblem beschrieben werden. Diese Methoden sind jedoch auf solche Datensätze beschränkt, bei denen die Anzahl der Beobachtungen die der Variablen übersteigt. Daher werden die Optimierungsprobleme modifiziert, um auf hochdimensionale Daten angewandt werden zu können, indem man einen Penalty-Term hinzufügt und die Kovarianz innerhalb der Klassen als Diagonalmatrix schätzt. So erhält man Penalized LDA und sparse discriminant analysis. Die Anwendung eines L1 Penalty-Terms führt bei diesen Methoden zu Sparse Models. Qualitätsmerkmale für die Modelle sind die Genauigkeit der Vorhersage der Klassenzugehörigkeiten sowie die Sparsity, welche durch die zuverlässige Identifikation der beeinflussenden Variablen und die Reduktion des Rauschanteils bewertet wird. Es wird eine Simulationsstudie durchgeführt, um die Stärken und Schwächen der Methoden zu untersuchen, wenn diese auf Daten mit einem hohen Rauschanteil angewendet werden. Weiters wird die Qualität der Modelle anhand von zwei Datensätzen aus Genexpressions-Experimenten bewertet.Linear discriminant analysis is a popular method for supervised classification, which performs well under various circumstances. In this thesis the equivalence of two linear classification methods is discussed in detail, namely Fisher's LDA and the optimal scoring approach, which is obtained from different optimization problems. These methods are limited to the analysis of data where the number of observations is higher than the number of predictor variables. Hence, the optimization problems are modified to be applicable in the high dimensional setting via penalization terms and diagonal within-class covariance estimates. The resulting methods are penalized LDA and sparse discriminant analysis, respectively. With an L1 penalization term sparse models are obtained with these methods. The criteria for the model quality are the prediction performance of the class memberships and the sparsity, which is evaluated by the identification of the influential variables and the reduction of the noise. A simulation study is conducted to investigate the strengths and weaknesses of the methods when applied to data with a high percentage of noise. Further, the quality of the models is evaluated for two gene expression data sets.7

Slavnov N. A. - One of the best experts on this subject based on the ideXlab platform.

  • Zero modes method and form factors in quantum integrable models
    'Elsevier BV', 2015
    Co-Authors: Pakuliak S., Ragoucy E., Slavnov N. A.
    Abstract:

    International audienceWe study integrable models solvable by the nested algebraic Bethe ansatz andpossessing $GL(3)$-invariant $R$-matrix. Assuming that the monodromy matrix ofthe model can be expanded into series with respect to the inverse spectralparameter, we define zero modes of the monodromy matrix entries as the firstnontrivial coefficients of this series. Using these zero modes we establish newrelations between form factors of the elements of the monodromy matrix. Weprove that all of them can be obtained from the form factor of a Diagonalmatrix element in special limits of Bethe parameters. As a result we obtaindeterminant representations for form factors of all the entries of themonodromy matrix

Tao Xianhua - One of the best experts on this subject based on the ideXlab platform.

  • diagonal one of real anti sub symmetric matrix
    Journal of Guangdong University of Technology, 2005
    Co-Authors: Tao Xianhua
    Abstract:

    The paper has discussed such problims as the properties of sub-eigenvalue and sub-eigenvector of real-anti-sub-symmetric matrix,and its diagonalization.Based on the above,the following result could be approached:If Ais a realanti-sub-symmetric matrix,then there exists a perpendicular matrix P.Multiplied with P and its reversal P~(ST)from the right and the left respectively,the matrix will become a Diagonalmatrix.

Pakuliak S. - One of the best experts on this subject based on the ideXlab platform.

  • Zero modes method and form factors in quantum integrable models
    'Elsevier BV', 2015
    Co-Authors: Pakuliak S., Ragoucy E., Slavnov N. A.
    Abstract:

    International audienceWe study integrable models solvable by the nested algebraic Bethe ansatz andpossessing $GL(3)$-invariant $R$-matrix. Assuming that the monodromy matrix ofthe model can be expanded into series with respect to the inverse spectralparameter, we define zero modes of the monodromy matrix entries as the firstnontrivial coefficients of this series. Using these zero modes we establish newrelations between form factors of the elements of the monodromy matrix. Weprove that all of them can be obtained from the form factor of a Diagonalmatrix element in special limits of Bethe parameters. As a result we obtaindeterminant representations for form factors of all the entries of themonodromy matrix