# KPLSR Models NIPALS Kernel PLSR algorithm described in Rosipal & Trejo (2001). The algorithm is slow for $n >= 500$. latin1 ```r kplsr(X, Y, weights = NULL, nlv, kern = "krbf", tol = .Machine$double.eps^0.5, maxit = 100, ...) ## S3 method for class 'Kplsr' transform(object, X, ..., nlv = NULL) ## S3 method for class 'Kplsr' coef(object, ..., nlv = NULL) ## S3 method for class 'Kplsr' predict(object, X, ..., nlv = NULL) ``` ## Arguments - `X`: For the main function: Training X-data ($n, p$). --- For the auxiliary functions: New X-data ($m, p$) to consider. - `Y`: Training Y-data ($n, q$). - `weights`: Weights ($n, 1$) to apply to the training observations. Internally, weights are "normalized" to sum to 1. Default to `NULL` (weights are set to $1 / n$). - `nlv`: The number(s) of LVs to calculate. --- For the auxiliary functions: The number(s) of LVs to consider. - `kern`: Name of the function defining the considered kernel for building the Gram matrix. See `krbf` for syntax, and other available kernel functions. - `tol`: Tolerance level for stopping the NIPALS iterations. - `maxit`: Maximum number of NIPALS iterations. - `...`: Optional arguments to pass in the kernel function defined in `kern` (e.g. `gamma` for `krbf`). - `object`: For the auxiliary functions: A fitted model, output of a call to the main function. ## Returns For `kplsr`: - **X**: Training X-data ($n, p$). - **Kt**: Gram matrix - **T**: X-scores matrix. - **C**: The Y-loading weights matrix. - **U**: intermediate output. - **R**: The PLS projection matrix (p,nlv). - **ymeans**: the centering vector of Y (q,1). - **weights**: vector of observation weights. - **kern**: kern function. - **dots**: Optional arguments. For `transform.Kplsr`: X-scores matrix for new X-data. For `coef.Kplsr`: - **int**: intercept values matrix. - **beta**: beta coefficient matrix. For `predict.Kplsr`: - **pred**: predicted values matrix for new X-data. ## References Rosipal, R., Trejo, L.J., 2001. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space. Journal of Machine Learning Research 2, 97-123. ## Note The second example concerns the fitting of the function sinc(x) described in Rosipal & Trejo 2001 p. 105-106 ## Examples ```r ## EXAMPLE 1 n <- 6 ; p <- 4 Xtrain <- matrix(rnorm(n * p), ncol = p) ytrain <- rnorm(n) Ytrain <- cbind(y1 = ytrain, y2 = 100 * ytrain) m <- 3 Xtest <- Xtrain[1:m, , drop = FALSE] Ytest <- Ytrain[1:m, , drop = FALSE] ; ytest <- Ytest[1:m, 1] nlv <- 2 fm <- kplsr(Xtrain, Ytrain, nlv = nlv, kern = "krbf", gamma = .8) transform(fm, Xtest) transform(fm, Xtest, nlv = 1) coef(fm) coef(fm, nlv = 1) predict(fm, Xtest) predict(fm, Xtest, nlv = 0:nlv)$pred pred <- predict(fm, Xtest)$pred msep(pred, Ytest) nlv <- 2 fm <- kplsr(Xtrain, Ytrain, nlv = nlv, kern = "kpol", degree = 2, coef0 = 10) predict(fm, Xtest, nlv = nlv) ## EXAMPLE 2 x <- seq(-10, 10, by = .2) x[x == 0] <- 1e-5 n <- length(x) zy <- sin(abs(x)) / abs(x) y <- zy + rnorm(n, 0, .2) plot(x, y, type = "p") lines(x, zy, lty = 2) X <- matrix(x, ncol = 1) nlv <- 2 fm <- kplsr(X, y, nlv = nlv) pred <- predict(fm, X)$pred plot(X, y, type = "p") lines(X, zy, lty = 2) lines(X, pred, col = "red") ```

kplsr function