sCCA: Sparse Canonical Correlation analysis

In sRDA: Sparse Redundancy Analysis

Description

Sparse Canonical Correlation analysis for high dimensional (biomedical) data. The function takes two datasets and returns a linear combination of maximally correlated canonical correlate pairs. Elastic net penalization (with its variants, UST, Ridge and Lasso penalization) is implemented for sparsity and smoothnesswith a built in cross validation procedure to obtain the optimal penalization parameters. It is possible to obtain multiple canonical variate pairs that are orthogonal to each other.

Usage

sCCA(predictor, predicted, penalization = "enet", ridge_penalty = 1,
  nonzero = 1, max_iterations = 100, tolerance = 1 * 10^-20,
  cross_validate = FALSE, parallel_CV = TRUE, nr_subsets = 10,
  multiple_LV = FALSE, nr_LVs = 1)

Arguments

predictor	The n*p matrix of the predictor data set
predicted	The n*q matrix of the predicted data set
penalization	The penalization method applied during the analysis (none, enet or ust)
ridge_penalty	The ridge penalty parameter of the predictor set's latent variable used for enet or ust (an integer if cross_validate = FALE, a list otherwise)
nonzero	The number of non-zero weights of the predictor set's latent variable (an integer if cross_validate = FALE, a list otherwise)
max_iterations	The maximum number of iterations of the algorithm
tolerance	Convergence criteria
cross_validate	K-fold cross validation to find best optimal penalty parameters (TRUE or FALSE)
parallel_CV	Run the cross validation parallel (TRUE or FALSE)
nr_subsets	Number of subsets for k-fold cross validation
multiple_LV	Obtain multiple latent variable pairs (TRUE or FALSE)
nr_LVs	Number of latent variables to be obtained

Value

An object of class "sRDA".

XI	Predictor set's latent variable scores
ETA	Predictive set's latent variable scores
ALPHA	Weights of the predictor set's latent variable
BETA	Weights of the predicted set's latent variable
nr_iterations	Number of iterations ran before convergence (or max number of iterations)
SOLVE_XIXI	Inverse of the predictor set's latent variable variance matrix
iterations_crts	The convergence criterion value (a small positive tolerance)
sum_absolute_betas	Sum of the absolute values of beta weights
ridge_penalty	The ridge penalty parameter used for the model
nr_nonzeros	The number of nonzero alpha weights in the model
nr_latent_variables	The number of latient variable pairs in the model
CV_results	The detailed results of cross validations (if cross_validate is TRUE)

Author(s)

Attila Csala

Examples

# generate data with few highly correlated variahbles
dataXY <- generate_data(nr_LVs = 2,
                           n = 250,
                           nr_correlated_Xs = c(5,20),
                           nr_uncorrelated_Xs = 250,
                           mean_reg_weights_assoc_X =
                             c(0.9,0.5),
                           sd_reg_weights_assoc_X =
                             c(0.05, 0.05),
                           Xnoise_min = -0.3,
                           Xnoise_max = 0.3,
                           nr_correlated_Ys = c(10,15),
                           nr_uncorrelated_Ys = 350,
                           mean_reg_weights_assoc_Y =
                             c(0.9,0.6),
                           sd_reg_weights_assoc_Y =
                             c(0.05, 0.05),
                           Ynoise_min = -0.3,
                           Ynoise_max = 0.3)

# seperate predictor and predicted sets
X <- dataXY$X
Y <- dataXY$Y

# run sRDA
CCA.res <- sCCA(predictor = X, predicted = Y, nonzero = 5,
ridge_penalty = 1, penalization = "ust")


# check first 10 weights of X
CCA.res$ALPHA[1:10]

## Not run: 
# run sRDA with cross-validation to determine best penalization parameters
CCA.res <- sCCA(predictor = X, predicted = Y, nonzero = c(5,10,15),
ridge_penalty = c(0.1,1), penalization = "enet", cross_validate = TRUE,
parallel_CV = TRUE)

# check first 10 weights of X
CCA.res$ALPHA[1:10]
CCA.res$ridge_penalty
CCA.res$nr_nonzeros

# obtain multiple latent variables
CCA.res <- sCCA(predictor = X, predicted = Y, nonzero = c(5,10,15),
ridge_penalty = c(0.1,1), penalization = "enet", cross_validate = TRUE,
parallel_CV = TRUE, multiple_LV = TRUE, nr_LVs = 2, max_iterations = 5)

# check first 10 weights of X in first two component
CCA.res$ALPHA[[1]][1:10]
CCA.res$ALPHA[[2]][1:10]

# latent variables are orthogonal to each other
t(CCA.res$XI[[1]]) %*% CCA.res$XI[[2]]


## End(Not run)

sRDA documentation built on May 2, 2019, 6:43 a.m.