seedCCA: Seeded Canonical correlation analysis
In seedCCA: Seeded Canonical Correlation Analysis
seedCCA R Documentation
Seeded Canonical correlation analysis
Description
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").
Usage
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<r. For type="seed2", if ux and uy are not NULL, they surpass u.
u
numeric, maximum number of projections. The default is 10. This is used for type="seed1", type="seed2" and tyepe="pls".
eps
numeric, the criteria to terminate iterative projections. The default is 0.01. If increment of projections is less than eps, then the iterative projection is terminated.
cut
numeric, between 0 and 1. The default is 0.9.
If d is NULL, cut is used for automatic replacements of cov(X,Y) and cov(Y,X) with their eigenvectors, depending on the value of cut. So, if any value of d is given, cut is not effective. cov(X,Y) and cov(Y,X) are replaced with their largest eigenvectors, whose cumulative eigenvalue proportion is bigger than the value of cut. This only works for type="seed2".
d
numeric, the user-selected number of largest eigenvectors of cov(X, Y) and cov(Y, X). The default is NULL. This only works for type="seed2". If any value of d is given, cut does not work.
AS
logical, status of automatic stop of projections. The default is TRUE. If TRUE, the iterative projection is automatically stopped, when the terminaion condition eps is satisfied. IfAS=FALSE, the iterative projections are stopped at the value of u.
scale
logical. scaling predictors to have zero mean and one standard deviation. The default is FALSE. If scale=TRUE, each predictor is scaled with mean 0 and variance 1 for partial least squares. This option works only for type="pls".
Details
Let p and r stand for the numbers of variables in the two sets and n stands for the sample size. The option of type="cca" can work only when max(p,r) < n, and seedCCA conducts standard canonical correlation analysis (Johnson and Wichern, 2007). If type="cca" is given and either p or r is equal to one, ordinary least squares (OLS) is done instead of canonical correlation analysis. If max(p,r) >= 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,r<n)
type="cca": subclass "seedols" (either p or r is equal to 1.)
type="seed1" and type="seed2": subclass "finalCCA" (max(p,r)>n)
type="pls": subclass "seedpls" (p>n and r <n)
So, plot(object) will result in different figure depending on the object.
The order of the values depending on type is follows.:
type="cca": standard CCA (max(p,r)<n, min(p,r)>1) / "finalCCA" subclass
type="cca": ordinary least squares (max(p,r)<n, min(p,r)=1) / "seedols" subclass
type="seed1": seeded CCA with case1 (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 r<n) / "seedpls" subclass
Value
type="cca"
Values with selecting type="cca": standard CCA (max(p,r)<n, min(p,r)>1) / "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, min(p,r)=1) / "seedols" subclass
coef
the estimated ordinary least squares coefficients
X
X, the first set
Y
Y, the second set
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 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<n) / "seedpls" subclass
coef
the estimated coefficients for each iterative projection upto u
u
the maximum number of projections
X
predictors
Y
response
scale
status of scaling predictors
cases
the number of observations
References
R. D. Cook, B. Li and F. Chiaromonte. Dimension reduction in regression without matrix inversion. Biometrika 2007; 94: 569-584.
Y. Im, H. Gang and JK. Yoo. High-throughput data dimension reduction via seeded canonical correlation analysis, J. Chemometrics 2015; 29: 193-199.
R. A. Johnson and D. W. Wichern. Applied Multivariate Statistical Analysis. Pearson Prentice Hall: New Jersey, USA; 6 edition. 2007; 539-574.
K. Lee and JK. Yoo. Canonical correlation analysis through linear modeling, AUST. NZ. J. STAT. 2014; 56: 59-72.
Examples
###### data(cookie) ######
data(cookie)
myseq<-seq(141,651,by=2)
X<-as.matrix(cookie[-c(23,61),myseq])
Y<-as.matrix(cookie[-c(23,61),701:704])
dim(X);dim(Y)
## standard CCA
fit.cca <-seedCCA(X[,1:4], Y, type="cca") ## standard canonical correlation analysis is done.
plot(fit.cca)
## ordinary least squares
fit.ols1 <-seedCCA(X[,1:4], Y[,1], type="cca") ## ordinary least squares is done, because r=1.
fit.ols2 <-seedCCA(Y[,1], X[,1:4], type="cca") ## ordinary least squares is done, because p=1.
## seeded CCA with case 1
fit.seed1 <- seedCCA(X, Y, type="seed1") ## suggested proper value of u is equal to 3.
fit.seed1.ux <- seedCCA(X, Y, ux=6, type="seed1") ## iterative projections done 6 times.
fit.seed1.uy <- seedCCA(Y, X, uy=6, type="seed1", AS=FALSE) ## projections not done until uy=6.
plot(fit.seed1)
## partial least squares
fit.pls1 <- seedCCA(X, Y[,1], type="pls")
fit.pls.m <- seedCCA(X, Y, type="pls") ## multi-dimensional response
par(mfrow=c(1,2))
plot(fit.pls1); plot(fit.pls.m)
######## data(nutrimouse) ########
data(nutrimouse)
X<-as.matrix(nutrimouse$gene)
Y<-as.matrix(nutrimouse$lipid)
dim(X);dim(Y)
## seeded CCA with case 2
fit.seed2 <- seedCCA(X, Y, type="seed2") ## d not specified, so cut=0.9 (default) used.
fit.seed2.99 <- seedCCA(X, Y, type="seed2", cut=0.99) ## cut=0.99 used.
fit.seed2.d3 <- seedCCA(X, Y, type="seed2", d=3) ## d is specified with 3.
## ux and uy specified, so proper values not suggested.
fit.seed2.uxuy <- seedCCA(X, Y, type="seed2", ux=10, uy=10)
plot(fit.seed2)
seedCCA documentation built on June 9, 2022, 9:05 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| seedCCA | R Documentation |
Seeded Canonical correlation analysis
Description
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").
Usage
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 |
ux |
numeric, maximum number of projections for X. The default is NULL. If this is not NULL, it surpasses the option |
uy |
numeric, maximum number of projections for Y. The default is NULL. If this is not NULL, it surpasses the option |
u |
numeric, maximum number of projections. The default is 10. This is used for |
eps |
numeric, the criteria to terminate iterative projections. The default is 0.01. If increment of projections is less than |
cut |
numeric, between 0 and 1. The default is 0.9.
If |
d |
numeric, the user-selected number of largest eigenvectors of cov(X, Y) and cov(Y, X). The default is NULL. This only works for |
AS |
logical, status of automatic stop of projections. The default is |
scale |
logical. scaling predictors to have zero mean and one standard deviation. The default is |
Details
Let p and r stand for the numbers of variables in the two sets and n stands for the sample size. The option of type="cca" can work only when max(p,r) < n, and seedCCA conducts standard canonical correlation analysis (Johnson and Wichern, 2007). If type="cca" is given and either p or r is equal to one, ordinary least squares (OLS) is done instead of canonical correlation analysis. If max(p,r) >= 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,r<n)
type="cca": subclass "seedols" (either p or r is equal to 1.)
type="seed1" and type="seed2": subclass "finalCCA" (max(p,r)>n)
type="pls": subclass "seedpls" (p>n and r <n)
So, plot(object) will result in different figure depending on the object.
The order of the values depending on type is follows.:
type="cca": standard CCA (max(p,r)<n, min(p,r)>1) / "finalCCA" subclass
type="cca": ordinary least squares (max(p,r)<n, min(p,r)=1) / "seedols" subclass
type="seed1": seeded CCA with case1 (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 r<n) / "seedpls" subclass
Value
type="cca" |
Values with selecting |
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 |
coef |
the estimated ordinary least squares coefficients |
X |
X, the first set |
Y |
Y, the second set |
type="seed1" |
Values with selecting |
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 |
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 |
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 |
coef |
the estimated coefficients for each iterative projection upto u |
u |
the maximum number of projections |
X |
predictors |
Y |
response |
scale |
status of scaling predictors |
cases |
the number of observations |
References
R. D. Cook, B. Li and F. Chiaromonte. Dimension reduction in regression without matrix inversion. Biometrika 2007; 94: 569-584.
Y. Im, H. Gang and JK. Yoo. High-throughput data dimension reduction via seeded canonical correlation analysis, J. Chemometrics 2015; 29: 193-199.
R. A. Johnson and D. W. Wichern. Applied Multivariate Statistical Analysis. Pearson Prentice Hall: New Jersey, USA; 6 edition. 2007; 539-574.
K. Lee and JK. Yoo. Canonical correlation analysis through linear modeling, AUST. NZ. J. STAT. 2014; 56: 59-72.
Examples
###### data(cookie) ###### data(cookie) myseq<-seq(141,651,by=2) X<-as.matrix(cookie[-c(23,61),myseq]) Y<-as.matrix(cookie[-c(23,61),701:704]) dim(X);dim(Y) ## standard CCA fit.cca <-seedCCA(X[,1:4], Y, type="cca") ## standard canonical correlation analysis is done. plot(fit.cca) ## ordinary least squares fit.ols1 <-seedCCA(X[,1:4], Y[,1], type="cca") ## ordinary least squares is done, because r=1. fit.ols2 <-seedCCA(Y[,1], X[,1:4], type="cca") ## ordinary least squares is done, because p=1. ## seeded CCA with case 1 fit.seed1 <- seedCCA(X, Y, type="seed1") ## suggested proper value of u is equal to 3. fit.seed1.ux <- seedCCA(X, Y, ux=6, type="seed1") ## iterative projections done 6 times. fit.seed1.uy <- seedCCA(Y, X, uy=6, type="seed1", AS=FALSE) ## projections not done until uy=6. plot(fit.seed1) ## partial least squares fit.pls1 <- seedCCA(X, Y[,1], type="pls") fit.pls.m <- seedCCA(X, Y, type="pls") ## multi-dimensional response par(mfrow=c(1,2)) plot(fit.pls1); plot(fit.pls.m) ######## data(nutrimouse) ######## data(nutrimouse) X<-as.matrix(nutrimouse$gene) Y<-as.matrix(nutrimouse$lipid) dim(X);dim(Y) ## seeded CCA with case 2 fit.seed2 <- seedCCA(X, Y, type="seed2") ## d not specified, so cut=0.9 (default) used. fit.seed2.99 <- seedCCA(X, Y, type="seed2", cut=0.99) ## cut=0.99 used. fit.seed2.d3 <- seedCCA(X, Y, type="seed2", d=3) ## d is specified with 3. ## ux and uy specified, so proper values not suggested. fit.seed2.uxuy <- seedCCA(X, Y, type="seed2", ux=10, uy=10) plot(fit.seed2)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.