Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables
暫譯: 光譜聚類與雙聚類：學習大型圖形與列聯表
Bolla, Marianna
- 出版商: Wiley
- 出版日期: 2013-08-26
- 售價: $3,210
- 貴賓價: 9.5 折 $3,050
- 語言: 英文
- 頁數: 292
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1118344928
- ISBN-13: 9781118344927
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相關主題
商品描述
Explores regular structures in graphs and contingency tables by spectral theory and statistical methods
This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs.
This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks.
Spectral Clustering and Biclustering:
- Provides a unified treatment for edge-weighted graphs and contingency tables via methods of multivariate statistical analysis (factoring, clustering, and biclustering).
- Uses spectral embedding and relaxation to estimate multiway cuts of edge-weighted graphs and bicuts of contingency tables.
- Goes beyond the expanders by describing the structure of dense graphs with a small spectral gap via the structural eigenvalues and eigen-subspaces of the normalized modularity matrix.
- Treats graphs like statistical data by combining methods of graph theory and statistics.
- Establishes a common outline structure for the contents of each algorithm, applicable to networks and microarrays, with unified notions and principles.
商品描述(中文翻譯)
透過光譜理論和統計方法探索圖形和列聯表中的規則結構
本書彌合了圖論和統計學之間的鴻溝，針對統計學家在面對大型加權圖或矩形陣列時所產生的挑戰性問題提供了解答。書中介紹了適用於生物學、社會學、通信網絡或微陣列的經典和現代統計方法，並提供了理論背景和證明。
本書適合用作研究生在資料探勘、多變量統計或應用圖論的一學期課程；但通過跳過證明，算法也可以被專家使用，這些專家只想在分析通信、社會或生物網絡時從數據中檢索信息。
光譜聚類和雙聚類：
- 通過多變量統計分析的方法（因子分析、聚類和雙聚類）對邊加權圖和列聯表提供統一的處理。
- 使用光譜嵌入和放鬆來估計邊加權圖的多路切割和列聯表的雙切割。
- 超越擴展器，通過結構特徵值和標準化模塊矩陣的特徵子空間描述具有小光譜間隙的稠密圖的結構。
- 將圖視為統計數據，結合圖論和統計學的方法。
- 為每個算法的內容建立共同的輪廓結構，適用於網絡和微陣列，並具有統一的概念和原則。
作者簡介
She is graduated from the Eötvös University of Budapest and holds a PhD (1984); further, a CSc degree (1993) from the Hungarian Academy of Sciences. Currently, she is a professor of the Institute of Mathematics, Budapest University of Technology and Economics and adjoint professor of the Central European University of Budapest. She also leads an undergraduate research course on Spectral Clustering in the Budapest Semester of Mathematics.
Her fields of expertise are multivariate statistics, applied graph theory, and data mining of social, biological, and communication networks. She has been working in various national and European research projects related to networks and data analysis.
She has published research papers in the Journal of Multivariate Analysis, Linear Algebra and Its Applications, Discrete Mathematics, Discrete Applied Mathematics, European Journal of Combinatorics, and the Physical Review E, among others.
She is the coauthor of the textbook in Hungarian: Bolla, M., Krámli, A., Theory of statistical inference, Typotex, Budapest (first ed. 2005, second ed. 2012) and another Hungarian book on multivariate statistical analysis. She was the managing editor of the book Contests in Higher Mathematics (ed. G. J. Székely), Springer, 1996.
作者簡介(中文翻譯)
她畢業於布達佩斯厄爾特大學，並於1984年獲得博士學位；此外，於1993年獲得匈牙利科學院的CSc學位。目前，她是布達佩斯科技經濟大學數學研究所的教授，以及布達佩斯中央歐洲大學的副教授。她還在布達佩斯數學學期中主導一門關於光譜聚類的本科研究課程。
她的專業領域包括多變量統計、應用圖論以及社會、生物和通信網絡的數據挖掘。她參與了多個與網絡和數據分析相關的國家和歐洲研究項目。
她在《多變量分析期刊》、《線性代數及其應用》、《離散數學》、《離散應用數學》、《歐洲組合學期刊》和《物理評論E》等期刊上發表了研究論文。
她是匈牙利語教科書的共同作者：Bolla, M., Krámli, A., 《統計推斷理論》，Typotex，布達佩斯（第一版2005年，第二版2012年），以及另一本關於多變量統計分析的匈牙利書籍。她曾擔任《高等數學競賽》一書的主編（編輯G. J. Székely），該書由Springer於1996年出版。
