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Algorithms of Scientometrics Including PageRank and its Generalization to the Interval Matrices

Alizadeh, Zahra | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44655 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahmoodian, Ebadollah
  7. Abstract:
  8. Due to the increasing number of research activities across the world,the academic societies are in the urgent need of appropriate criteria and methods for the evaluation of scientific publications. The term ‘Scientometrics’ has been coined to describe the methodology of aforementioned scientific assessment. Introduction of comprehensive and universal scientific rankings could provide inexperienced researchers with the opportunity to select most qualified publications for their literature reviews on the basis of such rankings. This procedure seems to be more convenient and reliable.In this framework, a review of most commonly used scientometric principles and methods are presented in the preliminary sections of this dissertation. PageRank algorithm is more exhaustively dealt with as it is one of most well known schemes on the case. This algorithm was first put forward by Larry Page and Sergey Brin at Stanford University to rank web pages by google search engine.There are special uncertainties in determination of the influential parameters of a scientific ranking. Interval matrices are by their nature capable of accounting for these uncertainties. Interval matrices with interval entries instead of real entries could provide an adequate interval treatment for scientometric variables and parameters. It can therefore be anticipated that the topic will be one of active research fields in scientomtrics during future years. Having considered the above mentioned factors,a part of present study has been devoted to investigating characteristics of interval matrices (Rohn, 2006 and Garloff, 2009). To this end, implementation of PageRank algorithm based on interval matrices is presented and discussed in detail (Ishii and
    Tempo, 2009)
  9. Keywords:
  10. Scientometrics ; Perron-Frobenious Theorem ; Pagerank Algorithm ; Interval Matrix

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  • مقدمه
  • علم‌سنجی
    • تعریف
    • شاخص‌‌های علم‌سنجی
      • ضریب تأثیر (IF)
      • شاخص فوریت (II)
      • شاخص اچ (H)
      • شاخص جی (G)
      • شاخص وای (Y)
      • ضریب ویژه (EF) و شاخص تأثیر مقاله (AI)
    • رده‌بندی‌های ارائه شده توسط کشورها
  • رتبه‌بندی پیج
    • تاریخچه
    • الگوریتم
    • کاربرد رتبه‌بندی پیج در دنیای فوتبال
  • ماتریس بازه‌ای
    • تعاریف و مفاهیم ابتدایی
      • مقدمه‌ای بر محاسبات بازه‌ای
      • توابع بازه‌ای
      • ماتریس بازه‌ای
    • دستگاه‌های خطی بازه‌ای مربعی
    • تعیین مقادیر و بردارهای ویژه‌ی ماتریس‌های بازه‌ای
    • تعیین خطای ناشی از لینک‌های شکننده روی مقادیر رتبه‌پیج
      • محاسبه‌ی کران‌های دقیق برای مقادیر رتبه‌پیج
      • تخمین مقادیر رتبه‌پیج بازه‌ای
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