# Sparse Partial Least Squares (sPLS) Function to perform sparse Partial Least Squares (sPLS). The sPLS approach combines both integration and variable selection simultaneously on two data sets in a one-step strategy. latin1 ```r sPLS(X, Y, ncomp, mode = "regression", max.iter = 500, tol = 1e-06, keepX = rep(ncol(X), ncomp), keepY = rep(ncol(Y), ncomp),scale=TRUE) ``` ## Arguments - `X`: Numeric matrix of predictors. - `Y`: Numeric vector or matrix of responses (for multi-response models). - `ncomp`: The number of components to include in the model (see Details). - `mode`: Character string. What type of algorithm to use, (partially) matching one of `"regression"` or `"canonical"`. See Details. - `max.iter`: Integer, the maximum number of iterations. - `tol`: A positive real, the tolerance used in the iterative algorithm. - `keepX`: Numeric vector of length `ncomp`, the number of variables to keep in $X$-loadings. By default all variables are kept in the model. - `keepY`: Numeric vector of length `ncomp`, the number of variables to keep in $Y$-loadings. By default all variables are kept in the model. - `scale`: a logical indicating if the orignal data set need to be scaled. By default `scale`=TRUE ## Details `sPLS` function fit sPLS models with $1, \ldots ,$`ncomp` components. Multi-response models are fully supported. The type of algorithm to use is specified with the `mode` argument. Two sPLS algorithms are available: sPLS regression `("regression")` and sPLS canonical analysis `("canonical")` (see References). ## Returns `sPLS` returns an object of class `"sPLS"`, a list that contains the following components: - **X**: The centered and standardized original predictor matrix. - **Y**: The centered and standardized original response vector or matrix. - **ncomp**: The number of components included in the model. - **mode**: The algorithm used to fit the model. - **keepX**: Number of $X$ variables kept in the model on each component. - **keepY**: Number of $Y$ variables kept in the model on each component. - **mat.c**: Matrix of coefficients to be used internally by `predict`. - **variates**: List containing the variates. - **loadings**: List containing the estimated loadings for the $X$ and $Y$ variates. - **names**: List containing the names to be used for individuals and variables. - **tol**: The tolerance used in the iterative algorithm, used for subsequent S3 methods - **max.iter**: The maximum number of iterations, used for subsequent S3 methods ## References Liquet Benoit, Lafaye de Micheaux Pierre, Hejblum Boris, Thiebaut Rodolphe. A group and Sparse Group Partial Least Square approach applied in Genomics context. **Submitted**. Le Cao, K.-A., Martin, P.G.P., Robert-Grani\', C. and Besse, P. (2009). Sparse canonical methods for biological data integration: application to a cross-platform study. **BMC Bioinformatics** 10 :34. Le Cao, K.-A., Rossouw, D., Robert-Grani\'e, C. and Besse, P. (2008). A sparse PLS for variable selection when integrating Omics data. **Statistical Applications in Genetics and Molecular Biology** 7 , article 35. Shen, H. and Huang, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. **Journal of Multivariate Analysis** 99 , 1015-1034. Tenenhaus, M. (1998). **La r\'egression PLS: th\'eorie et pratique**. Paris: Editions Technic. Wold H. (1966). Estimation of principal components and related models by iterative least squares. In: Krishnaiah, P. R. (editors), **Multivariate Analysis**. Academic Press, N.Y., 391-420. ## Author(s) Benoit Liquet and Pierre Lafaye de Micheaux. ## See Also `gPLS`, `sgPLS`, `predict`, `perf` and functions from `mixOmics` package: `summary`, `plotIndiv`, `plotVar`, `plot3dIndiv`, `plot3dVar`. ## Examples ```r ## Simulation of datasets X and Y with group variables n <- 100 sigma.gamma <- 1 sigma.e <- 1.5 p <- 400 q <- 500 theta.x1 <- c(rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 325)) theta.x2 <- c(rep(0, 320), rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 5)) theta.y1 <- c(rep(1, 15), rep(0, 5), rep(-1, 15), rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15), rep(0, 425)) theta.y2 <- c(rep(0, 420), rep(1, 15), rep(0, 5), rep(-1, 15) ,rep(0, 5), rep(1.5, 15), rep(0, 5), rep(-1.5, 15) , rep(0, 5)) Sigmax <- matrix(0, nrow = p, ncol = p) diag(Sigmax) <- sigma.e ^ 2 Sigmay <- matrix(0, nrow = q, ncol = q) diag(Sigmay) <- sigma.e ^ 2 set.seed(125) gam1 <- rnorm(n) gam2 <- rnorm(n) X <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% matrix(c(theta.x1, theta.x2), nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, p), sigma = Sigmax, method = "svd") Y <- matrix(c(gam1, gam2), ncol = 2, byrow = FALSE) %*% matrix(c(theta.y1, theta.y2), nrow = 2, byrow = TRUE) + rmvnorm(n, mean = rep(0, q), sigma = Sigmay, method = "svd") ind.block.x <- seq(20, 380, 20) ind.block.y <- seq(20, 480, 20) #### sPLS model model.sPLS <- sPLS(X, Y, ncomp = 2, mode = "regression", keepX = c(60, 60), keepY = c(60, 60)) result.sPLS <- select.spls(model.sPLS) result.sPLS$select.X result.sPLS$select.Y ```

sPLS function