# KRR-DA models Discrimination (DA) based on kernel ridge regression (KRR). latin1 ```r krrda(X, y, weights = NULL, lb = 1e-5, kern = "krbf", ...) ## S3 method for class 'Krrda' predict(object, X, ..., lb = 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 $1 / n$). - `lb`: A value of regularization parameter $lambda$. If `lb = 0`, a pseudo-inverse is used in the RR. - `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 ridge regression (KRR) 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 `krrda`: - **fm**: List with the outputs of the RR ((`X`): Training X-data ($n, p$); (`K`): Gram matrix; (`Kt`): Gram matrix; (`U`): intermediate output; (`UtDY`): intermediate output; (`sv`): singular values of the matrix (1,n); (`lb`): value of regularization parameter $lambda$; (`ymeans`): the centering vector of Y (q,1); (`weights`): the weights vector of X-variables (p,1); (`kern`): kern function; (`dots`): Optional arguments. - **lev**: y levels - **ni**: number of observations by level of y For `predict.Krrda`: - **pred**: matrix or list of matrices (if lb is a vector), with predicted class for each observation - **posterior**: matrix or list of matrices (if lb is a vector), 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] lb <- 1 fm <- krrda(Xtrain, ytrain, lb = lb) names(fm) predict(fm, Xtest) pred <- predict(fm, Xtest)$pred err(pred, ytest) predict(fm, Xtest, lb = 0:2) predict(fm, Xtest, lb = 0) ```

krrda function