Book contents
- Frontmatter
- Dedication
- Contents
- List of Algorithms
- Notation
- Preface
- I Classical Methods
- 1 Multidimensional Data
- 2 Principal Component Analysis
- 3 Canonical Correlation Analysis
- 4 Discriminant Analysis
- Problems for Part I
- II Factors and Groupings
- III Non-Gaussian Analysis
- Problems for Part III
- References
- Author Index
- Subject Index
- Data Index
3 - Canonical Correlation Analysis
from I - Classical Methods
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Dedication
- Contents
- List of Algorithms
- Notation
- Preface
- I Classical Methods
- 1 Multidimensional Data
- 2 Principal Component Analysis
- 3 Canonical Correlation Analysis
- 4 Discriminant Analysis
- Problems for Part I
- II Factors and Groupings
- III Non-Gaussian Analysis
- Problems for Part III
- References
- Author Index
- Subject Index
- Data Index
Summary
Alles Gescheite ist schon gedacht worden, man muß nur versuchen, es noch einmal zu denken (Johann Wolfgang von Goethe, Wilhelm Meisters Wanderjahre, 1749–1832.) Every clever thought has been thought before, we can only try to recreate these thoughts.
Introduction
In Chapter 2 we represented a random vector as a linear combination of uncorrelated vectors. From one random vector we progress to two vectors, but now we look for correlation between the variables of the first and second vectors, and in particular, we want to find out which variables are correlated and how strong this relationship is.
In medical diagnostics, for example, we may meet multivariate measurements obtained from tissue and plasma samples of patients, and the tissue and plasma variables typically differ. A natural question is: What is the relationship between the tissue measurements and the plasma measurements? A strong relationship between a combination of tissue variables and a combination of plasma variables typically indicates that either set of measurements could be used for a particular diagnosis. A very weak relationship between the plasma and tissue variables tells us that the sets of variables are not equally appropriate for a particular diagnosis.
On the share market, one might want to compare changes in the price of industrial shares and mining shares over a period of time. The time points are the observations, and for each time point, we have two sets of variables: those arising from industrial shares and those arising from mining shares.
- Type
- Chapter
- Information
- Analysis of Multivariate and High-Dimensional Data , pp. 70 - 115Publisher: Cambridge University PressPrint publication year: 2013