# Seeded Canonical correlation analysis The function `seedCCA` is mainly for implementing seeded canonical correlation analysis proposed by Im et al. (2015). The function conducts the following four methods, depending on the value of `type`. The option `type` has one of `c("cca", "seed1", "seed2", "pls")`. ```r seedCCA(X,Y,type="seed2",ux=NULL,uy=NULL,u=10,eps=0.01,cut=0.9,d=NULL,AS=TRUE,scale=FALSE) ``` ## Arguments - `X`: numeric vector or matrix (n * p), the first set of variables - `Y`: numeric vector or matrix (n * r), the second set of variables - `type`: character, a choice of methods among `c("cca", "seed1", "seed2", "pls")`. The default is `"seed2"`. - `ux`: numeric, maximum number of projections for X. The default is NULL. If this is not NULL, it surpasses the option `u` with `type="seed1"` and p>r. For `type="seed2"`, if `ux` and `uy` are not NULL, they surpass `u`. - `uy`: numeric, maximum number of projections for Y. The default is NULL. If this is not NULL, it surpasses the option `u` with `type="seed1"` and p= n, either `type="seed1"` or `type="seed2"` has to be chosen. This is the main purpose of `seedCCA`. If `type="seed1"`, only one set of variables, saying X with p for convenience, to have more variables than the other, saying Y with r, is initially reduced by the iterative projection approach (Cook et al. 2007). And then, the canonical correlation analysis of the initially-reduced X and the original Y is finalized. If `type="seed2"`, both X and Y are initially reduced. And then, the canonical correlation analysis of the two initially-reduced X and Y are finalzed. If `type="pls"`, partial least squares (PLS) is done. If `type="pls"` is given, the first set of variables in `seedCCA` is predictors and the second set is response. This matters The response can be multivariate. Depeding on the value of `type`, the resulted subclass by `seedCCA` are different.: `type="cca"`: subclass "finalCCA" (p >2; r >2; p,rn) `type="pls"`: subclass "seedpls" (p>n and r 1) / "finalCCA" subclass `type="cca"`: ordinary least squares (max(p,r)n and p>r) / "finalCCA" subclass `type="seed1"`: seeded CCA with case1 (max(p,r)>n and p<=r) / "finalCCA" subclass `type="seed2"`: seeded CCA with case2 (max(p,r)>n) / "finalCCA" subclass `type="pls"`: partial least squares (p>n and r1) / "finalCCA" subclass - **cor**: canonical correlations - **xcoef**: the estimated canonical coefficients for X - **ycoef**: the estimated canonical coefficients for Y - **Xscores**: the estimated canonical variates for X - **Yscores**: the estimated canonical variates for Y - **type="cca"**: Values with selecting `type="cca"`: ordinary least squares (max(p,r)n and p>r) / "finalCCA" subclass - **cor**: canonical correlations - **xcoef**: the estimated canonical coefficients for X - **ycoef**: the estimated canonical coefficients for Y - **proper.u**: a suggested proper number of projections for X - **initialMX0**: the initialized canonical coefficient matrices of X - **newX**: initially-reduced X - **Y**: the original Y - **Xscores**: the estimated canonical variates for X - **Yscores**: the estimated canonical variates for Y - **type="seed1"**: Values with selecting `type="seed1"`: seeded CCA with case1 (max(p,r)>n and p<=r) / "finalCCA" subclass) - **cor**: canonical correlations - **xcoef**: the estimated canonical coefficients for X - **ycoef**: the estimated canonical coefficients for Y - **proper.u**: a suggested proper number of projections for Y - **X**: the original X - **initialMY0**: the initialized canonical coefficient matrices of Y - **newY**: initially-reduced Y - **Xscores**: the estimated canonical variates for X - **Yscores**: the estimated canonical variates for Y - **type="seed2"**: Values with selecting `type="seed2"`: seeded CCA with case2 (max(p,r)>n) / "finalCCA" subclass - **cor**: canonical correlations - **xcoef**: the estimated canonical coefficients for X - **ycoef**: the estimated canonical coefficients for Y - **proper.ux**: a suggested proper number of projections for X - **proper.uy**: a suggested proper number of projections for Y - **d**: suggested number of eigenvectors of cov(X,Y) - **initialMX0**: the initialized canonical coefficient matrices of X - **initialMY0**: the initialized canonical coefficient matrices of Y - **newX**: initially-reduced X - **newY**: initially-reduced Y - **Xscores**: the estimated canonical variates for X - **Yscores**: the estimated canonical variates for Y - **type="pls"**: Values with selecting `type="pls"`:: partial least squares (p>n and r

seedCCA function