sCCA {sRDA}

Sparse Canonical Correlation 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)