Da Costa J.P. Rankings and Preferences: New Results in Weighted Correlation and Weighted Principal Component Analysis with Applications

Berlin: Springer, 2015. - 91p.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.The Weighted Rank Correlation Coefficient \(r_W\)
The Weighted Rank Correlation Coefficient \(r_{W2}\)
A Weighted Principal Component Analysis, WPCA1; Application to Gene Expression Data
A Weighted Principal Component Analysis (WPCA2) for Time Series Data
Weighted Clustering of Time Series