Canonical correlation analysis is a method for exploring the relationships between two multivariate sets of variables (vectors), all measured on the same individual. Consider, as an example, variables related to exercise and health.

Canonical transformations allow us to change the phase-space coordinate system that we use to express a problem, preserving the form of Hamilton’s equations. If we solve Hamilton’s equations in one phase-space coordinate system we can use the transformation to carry the solution to the other coordinate system.

A canonical variate is a new variable (variate) formed by making a linear combination of two or more variates (variables) from a data set. A linear combination of variables is the same as a weighted sum of variables.

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero.

The PCA+regression you conceive of is two-step, initially “unsupervised” (“blind”, as you said) strategy, while CCA is one-step, “supervised” strategy. Both are valid – each in own investigatory settings! 1st principal component (PC1) obtained in PCA of set Y is a linear combination of Y variables.

In applied statistics, canonical correspondence analysis (CCA) is a multivariate constrained ordination technique that extracts major gradients among combinations of explanatory variables in a dataset. The requirements of a CCA are that the samples are random and independent.

To perform classical CCA, we use cancor() function CCA R package. cancor() function computes canonical covariates between two input data matrices. By default cancor() centers the columns of data matrices. cancor() function returns a list containing the correlation between the variables and the coefficients.

In order to use Canonical Correspondence Analysis, one needs:

1. A contingency table X that contains the frequencies of a series of objects (in ecology species), on the several sites where they are counted,
2. A table Y of descriptive variables that are measured on the same sites.

A Canonical loading measures the simple linear correlation between an original observed variable in the u- or v-variable set and that set’s canonical variate. Canonical loadings are discussed further below in the section entitled “Interpreting the Canonical Variates.”

SPSS performs canonical correlation using the manova command. Don’t look for manova in the point-and-click analysis menu, its not there. The manova command is one of SPSS’s hidden gems that is often overlooked. Used with the discrim option, manova will compute the canonical correlation analysis.

Redundancy analysis (RDA) is a method to extract and summarise the variation in a set of response variables that can be explained by a set of explanatory variables.

Redundancy analysis (RDA) is similar to canonical correlation analysis but allows the user to derive a specified number of synthetic variables from one set of (independent) variables that explain as much variance as possible in another (independent) set. It is a multivariate analogue of regression.

Principal component analysis (PCA), correspondence analysis (CA), discriminant analysis (DA) and non-metric multidimensional scaling (NMDS) can be used to analyse data without explanatory variables, whereas canonical correspondence analysis (CCA) and redundancy analysis (RDA) use both response and explanatory variables …

RDA. RDA: combines regression and PCA, it is an extension of regression analysis to model multivariate response data. RDA computes axes that are linear combinations of the explanatory variables (in order of which explain the most variation of the species matrix). The axes are orthogonal to eachother (i.e. right angles) …

rda) is a format designed for use with R, a system for statistical computation and related graphics, for storing a complete R workspace or selected “objects” from a workspace in a form that can be loaded back by R. The save function in R has options that result in significantly different variants of the format.

Redundancy Analysis allows to obtain a simultaneous representation of the observations, the Y variables, and the X variables in two or three dimensions, that is optimal for a covariance criterion (Ter Braak 1986).

Redundancy analysis (RDA) is an extension of multiple linear regression (MLR) that accounts for multiple response variables as well as multiple explanatory variables. That is, the RDA axes and linear combinations of your explanatory variables should be maximally ‘redundant’.

Distance-based redundancy analysis (dbRDA) is a method for carrying out constrained ordinations on data using non-Euclidean distance measures. The usual methods for constrained ordinations (CCA, RDA) use Euclidean distance, but this does not work for all data (such as community count data).

Redundancy Analysis allows studying the relationship between two tables of variables Y and X. While the Canonical Correlation Analysis is a symmetric method, Redundancy Analysis is non-symmetric. In Canonical Correlation Analysis, the components extracted from both tables are such that their correlation is maximized.

The RDA was run four times within each combination of environmental variable groups. The partial RDA is in fact a residual analysis in which the relation between responder and explanatory variable is analysed after the influence of the `covariables’ has been removed.

Canonical analysis is a multivariate technique which is concerned with determining the relationships between groups of variables in a data set. The purpose of canonical analysis is then to find the relationship between X and Y, i.e. can some form of X represent Y.

Canonical cross-loadings for y variables on the y scores for each canonical variate. xcrosscorrsq. Squared canonical cross-loadings for x variables on the y scores for each canonical variate (i.e., the fraction of variance in each x variable attributable to y through the respective CVs).

The discriminant command in SPSS performs canonical linear discriminant analysis which is the classical form of discriminant analysis. In this example, we specify in the groups subcommand that we are interested in the variable job, and we list in parenthesis the minimum and maximum values seen in job.