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Eine Methode für Vollständig Positive und Nichtnegative Matrixzerlegungen
Get PDFA matrix A is called completely positive if there exists an entrywise nonnegative matrix B such that A = BB^T. These matrices can be used to obtain convex reformulations of for example nonconvex quadratic or combinatorial problems. One of the main problems with completely positive matrices is checking whether a given matrix is completely positive. This is known to be NP-hard in general. rnrnFor a given matrix completely positive matrix A, it is nontrivial to find a cp-factorization A=BB^T with nonnegative B since this factorization would provide a certificate for the matrix to be completely positive. But this factorization is not only important for the membership to the completely positive cone, it can also be used to recover the solution of the underlying quadratic or combinatorial problem. In addition, it is not a priori known how many columns are necessary to generate a cp-factorization for the given matrix. The minimal possible number of columns is called the cp-rank of A and so far it is still an open question how to derive the cp-rank for a given matrix. Some facts on completely positive matrices and the cp-rank will be given in Chapter 2. Moreover, in Chapter 6, we will see a factorization algorithm, which, for a given completely positive matrix A and a suitable starting point, computes the nonnegative factorization A=BB^T. The algorithm therefore returns a certificate for the matrix to be completely positive. As introduced in Chapter 3, the fundamental idea of the factorization algorithm is to start from an initial square factorization which is not necessarily entrywise nonnegative, and extend this factorization to a matrix for which the number of columns is greater than or equal to the cp-rank of A. Then it is the goal to transform this generated factorization into a cp-factorization. This problem can be formulated as a nonconvex feasibility problem, as shown in Section 4.1, and solved by a method which is based on alternating projections, as proven in Chapter 6. On the topic of alternating projections, a survey will be given in Chapter 5. Here we will see how to apply this technique to several types of sets like subspaces, convex sets, manifolds and semialgebraic sets. Furthermore, we will see some known facts on the convergence rate for alternating projections between these types of sets. Considering more than two sets yields the so called cyclic projections approach. Here some known facts for subspaces and convex sets will be shown. Moreover, we will see a new convergence result on cyclic projections among a sequence of manifolds in Section 5.4. In the context of cp-factorizations, a local convergence result for the introduced algorithm will be given. This result is based on the known convergence for alternating projections between semialgebraic sets. To obtain cp-facrorizations with this first method, it is necessary to solve a second order cone problem in every projection step, which is very costly. Therefore, in Section 6.2, we will see an additional heuristic extension, which improves the numerical performance of the algorithm. Extensive numerical tests in Chapter 7 will show that the factorization method is very fast in most instances. In addition, we will see how to derive a certificate for the matrix to be an element of the interior of the completely positive cone. As a further application, this method can be extended to find a symmetric nonnegative matrix factorization, where we consider an additional low-rank constraint. Here again, the method to derive factorizations for completely positive matrices can be used, albeit with some further adjustments, introduced in Section 8.1. Moreover, we will see that even for the general case of deriving a nonnegative matrix factorization for a given rectangular matrix A, the key aspects of the completely positive factorization approach can be used. To this end, it becomes necessary to extend the idea of finding a completely positive factorization such that it can be used for rectangular matrices. This yields an applicable algorithm for nonnegative matrix factorization in Section 8.2. Numerical results for this approach will suggest that the presented algorithms and techniques to obtain completely positive matrix factorizations can be extended to general nonnegative factorization problems.Viele nicht konvexe Optimierungsprobleme können als konvexes Problem über dem Kegel der vollständig positiven Matrizen reformuliert werden, sodass für diese Reformulierung lokale und globale Optima zusammenfallen. Dies ist möglich, da die Komplexität des Problems nun vollständig in der Kegelnebenbedingung enthalten ist. Daher ist es nicht verwunderlich, dass die Überprüfung der Zugehörigkeit einer Matrix zum vollständig positiven Kegel NP-schwer ist. Als Hauptresultat dieser Arbeit werden wir sehen, wie algorithmisch ein Zertifikat generiert werden kann, welches für geeignete Startwerte verifiziert, dass eine gegebene Matrix vollständig positiv ist. Als fundamentale Definition gilt hier, dass eine Matrix A vollständig positiv ist, falls es eine Zerlegungsmatrix B gibt, die eintragsweise nichtnegativ ist und die Gleichung A=BB^T erfüllt. Eine solche Zerlegung liefert daher immer ein Zertifikat, welches zeigt, dass die gegebene Matrix vollständig positiv ist. Basierend auf dieser Definition werden wir einige Fakten zu diesen Zerlegungen sehen, die nichtzuletzt auch für die praktischen Anwendungen relevant sind und daher durch diese motiviert werden können. Basierend auf diesen Zerlegungen ist es zusätzlich möglich, weitere Bedingungen für vollständig positive Matrizen abzuleiten. Hier ist es insbesondere notwendig mit einer passenden Startzerlegung der Matrix zu beginnen. Wie eine solche Zerlegung generiert werden kann, wird ebenfalls gezeigt. Hier werden wir insbesondere auf orthognale Matrizen als Werkzeug zurückgreifen. So ist es insgesamt möglich, das Problem der Verifizierung der Zugehörigkeit einer Matrix zum vollständig positiven Kegel auf ein Zulässigkeitsproblem zu reduzieren. Im Detail ist es dazu notwendig, eine Matrix im Schnitt eines polyedrischen Kegels und dem nichtnegativen Orthanten zu finden. Dabei werden wir auf die auf von Neumann zurückgehende Technik der alternierenden Projektionen zurückgreifen, um eine solche Matrix zu generieren. Für dieses Verfahren wird eine kurze Einführung und Erläuterung der Anwendung auf verschiedene Typen von Mengen gegeben. Insbesondere werden anhand von geometrischen Eigenschaften bekannte Resultate bezüglich der Konvergenz des Verfahrens und deren Geschwindigkeit gezeigt. Erweitert man die Idee der alternierenden Projektionen auf mehr als zwei Mengen, so spricht man vom zyklischen Projektions-Verfahren. Auch für diesen Ansatz werden bekannte Resultate für Unterräume und allgemeine konvexe Mengen gezeigt. Des Weiteren wird ein neues Konvergenzresultat für die zyklische Projektion zwischen transversalen Mannigfaltigkeiten hergeleitet, welches auf den bekannten Resultaten für die alternierenden Projektionen auf Mannigfaltigkeiten basiert. Insbesondere lässt sich die Methode der alternierenden Projektionen auf semialgebraische Mengen anwenden. Dieses Resultat werden wir nutzen, um einen ersten Algorithmus zur Generierung von Zerlegungen von vollständig positiven Matrizen herzuleiten. Für diesen Algorithmus ist es möglich, ein lokales Konvergenzresultat zu zeigen. Insbesondere greift dieser Algorithmus jedoch auf das wiederholte Lösen von second order cone Problemen zurück. Diese sind zwar in polynomieller Zeit lösbar, aber immer noch vergleichsweise rechenintensiv. Aus diesem Grund werden wir eine modifizierte Variante dieses Algorithmus sehen, die ohne diese speziellen Probleme auskommt. Hier verlieren wir zwar das lokale Konvergenzresultat, aber numerische Experimente zeigen, dass dieser Ansatz für nahezu alle getesteten Beispiele vollständig positiver Matrizen in sehr kurzer Zeit eine Zerlegung liefert. Neben der Generierung von Zerlegungen für vollständig positive Matrizen können die gezeigten Methoden und Verfahren auch im Kontext der sogenannten Nichtnegativen Matrix Zerlegung angewandt werden. Hier werden wir sehen, dass für die symmetrische Variante dieser Zerlegung lediglich zusätzliche niedrig-Rang Nebenbedingungen integriert werden müssen. Für den allgemeinen, nicht symmetrischen Fall hingegen können zwar die Ansätze der Verfahren zur Generierung von Zerlegungen für vollständig positive Matrizen verwendet werden, müssen aber auf nicht-quadratische Ausgangsmatrizen erweitert werden. Hier werden wir sehen, dass orthogonale Matrizen nicht mehr das Werkzeug der Wahl sind und entsprechend ersetzt werden müssen. Des Weiteren ist es nicht mehr möglich auf den Ansatz der alternierenden Projektionen zurückzugreifen, da die dazu notwendigen Projektionen nicht mehr berechnet werden können. Nichtsdestotrotz ist es möglich, die Ideen des modifizierten Algorithmus für vollständig positive Matrizen auch in diesem Kontext zu verwenden. Sowohl für den symmetrischen, als auch für den allgemeinen Fall der nichtnegativen Matrixzerlegung, werden wir zahlreiche numerische Experimente sehen, die die Anwendbarkeit der in dieser Arbeit generierten Algorithmen auch in diesem Kontext untermauern
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
Author Under Sail The Imagination of Jack London, 1893-1902
No full textIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Intro -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgments -- Introduction -- 1. Spirit Truth -- 2. From Absorption to Theatricality and Back Again -- 3. "I Will Build a New Present" -- 4. Sons as Authors -- 5. Fathers as Publishers -- 6. The Daughter as Author -- 7. Lovers as Authors -- 8. At Sea with the Family -- 9. Yellow News, Yellow Stories -- 10. The Return Home -- Notes -- Bibliography -- Index -- About Jay WilliamsIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Description based on publisher supplied metadata and other sources.Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, YYYY. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
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