Rankings and preferences : new results in weighted correlation and weighted principal component analysis with applications /: new results in weighted correlation and weighted principal component analysis with applications. ([2015])

• Record Type: Book
• Further Information: Note: Joaquim Pinto da Costa.
• Authors: Costa, Joaquim Pinto da
• Contents: Preface; Contents; 1 Introduction; 1.1 Some Motivating Applications; 1.2 Weighted Correlation and Applications; 1.3 Organization of the Book; 2 The Weighted Rank Correlation Coefficient rW; 2.1 Introduction; 2.2 Rank Correlation; 2.3 Weighted Rank Measure of Correlation; 2.4 Properties of the Distribution of rW Under the Null Hypothesis of Independence; 2.4.1 Linear Rank Statistics; 2.4.2 Exact and Asymptotic Distribution of rW Under the Null Hypothesis of Independence; 2.4.3 Simulations; 2.4.4 Comparison Between rW and rS; 2.5 The Asymptotic Distribution of rW for the General Case. 2.5.1 sum3i=1Ain is Asymptotically Normal Distributed 2.5.2 B*1n is Asymptotically Negligible ; 2.5.3 rW is Asymptotically Normal Distributed ; 2.6 Examples of Application of rW ; 2.7 Conclusions About rW; 3 The Weighted Rank Correlation Coefficient rW2; 3.1 Introduction; 3.2 The Formula of the Coefficient rW2 in the Case of Ties; 3.3 Comparison Between the Three Coefficients rW2, rW and rS; 3.4 A New Way of Developing Weighted Correlation Coefficients; 4 A Weighted Principal Component Analysis, WPCA1; Application to Gene Expression Data; 4.1 Introduction. 4.2 A New Weighted Version of PCA4.3 Preliminary Version of Weighted Principal Component Analysis Using rW; 4.4 Weighted Principal Component Analysys, WPCA1, Using rW2; 4.4.1 Robustness to Outliers and Noise; 4.5 A New Method for Selecting Relevant Genes in Microarray Data; 4.5.1 Support Vector Machines Classification: Results for Genes Chosen with SAM, PDeig, and with Our Method for WPCA and PCA; 4.5.2 Analysis of the Chosen Genes; 4.6 Conclusions; 5 A Weighted Principal Component Analysis (WPCA2) for Time Series Data; 5.1 Introduction; 5.2 Motivation and Definition. 5.3 Weight Functions: Examples5.4 Applications; 5.5 Final Remarks; 6 Weighted Clustering of Time Series; 6.1 Introduction; 6.2 Applications; Appendix; References.
• Publisher Details: Heidelberg [Germany] : Springer
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 519.536; Correlation (Statistics); MATHEMATICS -- Applied; MATHEMATICS -- Probability & Statistics -- General; Correlation (Statistics); Electronic books
• Languages: English
• ISBNs: 9783662483442; 3662483440; 3662483432; 9783662483435
• Related ISBNs: 9783662483435
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.