| Title: | Sparse Redundancy Analysis |
| Version: | 1.0.0 |
| Date: | 2017-12-12 |
| Author: | Attila Csala [aut, cre], Koos Zwinderman [ctb] |
| Maintainer: | Attila Csala <a@csala.me> |
| Description: | Sparse redundancy analysis for high dimensional (biomedical) data. Directional multivariate analysis to express the maximum variance in the predicted data set by a linear combination of variables of the predictive data set. Implemented in a partial least squares framework, for more details see Csala et al. (2017) <doi:10.1093/bioinformatics/btx374>. |
| Depends: | R (≥ 2.7), Matrix, doParallel, elasticnet, foreach, mvtnorm |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-12-14 10:24:28 UTC; acsala |
| Repository: | CRAN |
| Date/Publication: | 2017-12-14 13:36:54 UTC |
sRDA.
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)
Generate data sets for sparse multivariate analysis
Description
Generate two data sets with highly correlated and noise variables modeled in a multiple latent variable structure. The latent variables are orthogonal to each other thus capture a different portion of association between the involved data sets. Thu function generates data that can be used to verify sRDA's ability of finding the highly correlated variables accross multiple latent variables.
Usage
generate_data(nr_LVs = 1, n = 50, nr_correlated_Xs = c(5),
nr_uncorrelated_Xs = 250, mean_reg_weights_assoc_X = c(0.7),
sd_reg_weights_assoc_X = c(0.05), Xnoise_min = -0.3, Xnoise_max = 0.3,
nr_correlated_Ys = c(5), nr_uncorrelated_Ys = 350,
mean_reg_weights_assoc_Y = c(0.7), sd_reg_weights_assoc_Y = c(0.05),
Ynoise_min = -0.3, Ynoise_max = 0.3)
Arguments
nr_LVs |
The number of latent variables between the predicitve and predicted data sets. The latent variables model the association between data sets. |
n |
The number of observations (rows) in the data sets. |
nr_correlated_Xs |
Number of variables of the predictive data set that are associated with the latent variables. |
nr_uncorrelated_Xs |
Number of variables of the predictive data set that is not associated with the latent variables. |
mean_reg_weights_assoc_X |
Mean of the regression weights of the predictive varaibles that are associated with the latent variables. |
sd_reg_weights_assoc_X |
Standard deviation of the regression weights of the predictive varaibles that are associated with the latent variables. |
Xnoise_min |
The lower bound of the unifrom distribution that is used to sample the values for the regression weights of the predictive varaibles that are not associated with the latent variables. |
Xnoise_max |
The upper bound of the unifrom distribution that is used to sample the values for the regression weights of the predictive varaibles that are not associated with the latent variables. |
nr_correlated_Ys |
Number of variables of the predictive data set that are associated with the latent variables. |
nr_uncorrelated_Ys |
Number of variables of the predicted data set that is not associated with the latent variables. |
mean_reg_weights_assoc_Y |
Mean of the regression weights of the predicted varaibles that are associated with the latent variables. |
sd_reg_weights_assoc_Y |
Standard deviation of the regression weights of the predicted varaibles that are associated with the latent variables. |
Ynoise_min |
The lower bound of the unifrom distribution that is used to sample the values for the regression weights of the predicted varaibles that are not associated with the latent variables. |
Ynoise_max |
The upper bound of the unifrom distribution that is used to sample the values for the regression weights of the prediced varaibles that are not associated with the latent variables. |
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
dim(X);dim(Y)
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)