# KPLSR-DA models Discrimination (DA) based on kernel PLSR (KPLSR) latin1 ```r kplsrda(X, y, weights = NULL, nlv, kern = "krbf", ...) ## S3 method for class 'Kplsrda' predict(object, X, ..., nlv = NULL) ``` ## Arguments - `X`: For main function: Training X-data ($n, p$). --- For auxiliary function: New X-data ($m, p$) to consider. - `y`: Training class membership ($n$). Note: If `y` is a factor, it is replaced by a character vector. - `weights`: Weights ($n$) to apply to the training observations for the PLS2. Internally, weights are "normalized" to sum to 1. Default to `NULL` (weights are set to $1 / n$). - `nlv`: For main function: The number(s) of LVs to calculate. --- For auxiliary function: 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. - `...`: Optional arguments to pass in the kernel function defined in `kern` (e.g. `gamma` for `krbf`). - `object`: For auxiliary function: A fitted model, output of a call to the main functions. ## Details The training variable $y$ (univariate class membership) is transformed to a dummy table containing $nclas$ columns, where $nclas$ is the number of classes present in $y$. Each column is a dummy variable (0/1). Then, a kernel PLSR (KPLSR) is run on the $X-$data and the dummy table, returning predictions of the dummy variables. For a given observation, the final prediction is the class corresponding to the dummy variable for which the prediction is the highest. ## Returns For `kplsrda`: - **fm**: list with the kplsrda model: (`X`): the training X-data ($n, p$); (`Kt`): the 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. - **lev**: y levels - **ni**: number of observations by level of y For `predict.Kplsrda`: - **pred**: predicted class for each observation - **posterior**: calculated probability of belonging to a class for each observation ## Examples ```r n <- 50 ; p <- 8 Xtrain <- matrix(rnorm(n * p), ncol = p) ytrain <- sample(c(1, 4, 10), size = n, replace = TRUE) m <- 5 Xtest <- Xtrain[1:m, ] ; ytest <- ytrain[1:m] nlv <- 2 fm <- kplsrda(Xtrain, ytrain, nlv = nlv) names(fm) predict(fm, Xtest) pred <- predict(fm, Xtest)$pred err(pred, ytest) predict(fm, Xtest, nlv = 0:nlv)$posterior predict(fm, Xtest, nlv = 0)$posterior predict(fm, Xtest, nlv = 0:nlv)$pred predict(fm, Xtest, nlv = 0)$pred ```

kplsrda function