sRDA: sRDA.

In sRDA: Sparse Redundancy Analysis

Description

sRDA.

Sparse Redundancy Analysis (sRDA) to express the maximum variance in the predicted data set by a linear combination of variables (latent variable) of the predictive data set. Elastic net penalization (with its variants, UST, Ridge and Lasso penalization) is implemented for sparsity and smoothness with a built in cross validation procedure to obtain the optimal penalization parameters. It is possible to obtain multiple latent variables which are orthogonal to each other, thus each explaining a different protion of variance in the predicted data set. sRDA is implemented in a Partial Least Squares framework, for more details see Csala et al. (2017).

Usage

sRDA(predictor, predicted, penalization = "enet", ridge_penalty = 1,
  nonzero = 1, max_iterations = 100, tolerance = 1 * 10^-20,
  cross_validate = FALSE, parallel_CV = FALSE, 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 (an integer if cross_validate = FALSE, a list otherwise)
nonzero	The number of non-zero weights of the predictor set's latent variable used for enet or ust (an integer if cross_validate = FALSE, a list otherwise)
max_iterations	The maximum number of iterations of the algorithm (integer)
tolerance	Convergence criteria (number, a small positive tolerance)
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 (integer, the value for k)
multiple_LV	Obtain multiple latent variable pairs (TRUE or FALSE)
nr_LVs	Number of latent variable pairs (components) to be obtained (integer)

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 (components) in the model
CV_results	The detailed results of cross validations (if cross_validate is TRUE)

Author(s)

Attila Csala

References

Csala A., Voorbraak F.P.J.M., Zwinderman A.H., and Hof M.H. (2017) Sparse redundancy analysis of high-dimensional genetic and genomic data. Bioinformatics, 33, pp.3228-3234. https://doi.org/10.1093/bioinformatics/btx374

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


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

## Not run: 
# run sRDA with cross-validation to determine best penalization parameters
RDA.res <- sRDA(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
RDA.res$ALPHA[1:10]

# check the Ridge parameter and the number of nonzeros included in the model
RDA.res$ridge_penalty
RDA.res$nr_nonzeros

# check how much time the cross validation did take
RDA.res$CV_results$stime

# obtain multiple latent variables (components)
RDA.res <- sRDA(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 20 weights of X in first two component
RDA.res$ALPHA[[1]][1:20]
RDA.res$ALPHA[[2]][1:20]

# components are orthogonal to each other
t(RDA.res$XI[[1]]) %*% RDA.res$XI[[2]]


## End(Not run)

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