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Rankings and Preferences

New Results in Weighted Correlation and Weighted Principal Component Analysis with Applications

  • Book
  • © 2015

Overview

Authors:
  1. Joaquim Pinto da Costa

    1. Department of Mathematics, University of Porto, Porto, Portugal

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  • Numerous applications help the reader to learn quickly
  • Contains two special chapters on two very popular weighted correlation coefficients
  • Describes an easy way of using weighted correlation with already existing statistical software
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • Joaquim Pinto da Costa
    Pages 1-7

  3. The Weighted Rank Correlation Coefficient \(r_W\)

    • Joaquim Pinto da Costa
    Pages 9-27

  4. The Weighted Rank Correlation Coefficient \(r_{W2}\)

    • Joaquim Pinto da Costa
    Pages 29-38

  5. A Weighted Principal Component Analysis, WPCA1; Application to Gene Expression Data

    • Joaquim Pinto da Costa
    Pages 39-53

  6. A Weighted Principal Component Analysis (WPCA2) for Time Series Data

    • Joaquim Pinto da Costa
    Pages 55-67

  7. Weighted Clustering of Time Series

    • Joaquim Pinto da Costa
    Pages 69-73

  8. Back Matter

    Pages 75-91
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Keywords

About this book

This book examines in detail the correlation, more precisely the weighted correlation and applications involving rankings. A general application is the evaluation of methods to predict rankings. Others involve rankings representing human preferences to infer user preferences; the use of weighted correlation with microarray data and those in the domain of time series. In this book we present new weighted correlation coefficients and new methods of weighted principal component analysis.

We also introduce new methods of dimension reduction and clustering for time series data and describe some theoretical results on the weighted correlation coefficients in separate sections.

Reviews

“This book describes newly developed methods of weighted correlation by the author and his collaborators. … This book is useful for those who want to learn a series of studies on weighted correlations by the author and his collaborators.” (Hidehiko Kamiya, Mathematical Reviews, August, 2016)

Authors and Affiliations

  • Department of Mathematics, University of Porto, Porto, Portugal

    Joaquim Pinto da Costa

About the author

Joaquim Pinto da Costa received his first degree in Applied Mathematics from Porto Universitiy (Portugal), his M. Sc. degree in Applied Statistics from Oxford University and his Ph.D. degree in Applied Mathematics from University of Rennes II (France). Since 199, he is Assistant Professor at the Mathematics Department of Porto University. His research interests include Statistics, Statistical Learning Theory, Pattern Recognition, Discriminant Analysis and Clustering, Data Analysis, Neural Networks, SVMs and Machine Learning.

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