# KNN-R KNN weighted regression. For each new observation to predict, a number of $k$ nearest neighbors is selected and the prediction is calculated by the average (eventually weighted) of the response $Y$ over this neighborhood. latin1 ```r knnr(X, Y, nlvdis, diss = c("eucl", "mahal"), h, k) ## S3 method for class 'Knnr' predict(object, X, ...) ``` ## 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 ($n, q$). - `nlvdis`: The number of LVs to consider in the global PLS used for the dimension reduction before calculating the dissimilarities. If `nlvdis = 0`, there is no dimension reduction. (see details) - `diss`: The type of dissimilarity used for defining the neighbors. Possible values are "eucl" (default; Euclidean distance), "mahal" (Mahalanobis distance), or "correlation". Correlation dissimilarities are calculated by sqrt(.5 * (1 - rho)). - `h`: A scale scalar defining the shape of the weight function. Lower is $h$, sharper is the function. See `wdist`. - `k`: The number of nearest neighbors to select for each observation to predict. - `object`: --- For the auxiliary functions: A fitted model, output of a call to the main function. - `...`: --- For the auxiliary functions: Optional arguments. Not used. ## Details In function `knnr`, the dissimilarities used for computing the neighborhood and the weights can be calculated from the original X-data or after a dimension reduction (argument `nlvdis`). In the last case, global PLS scores are computed from $(X, Y)$ and the dissimilarities are calculated on these scores. For high dimension X-data, the dimension reduction is in general required for using the Mahalanobis distance. ## Returns For `knnr`:list with input arguments. For `predict.Knnr`: - **pred**: prediction calculated for each observation by the average (eventually weighted) of the response $Y$ over its neighborhood. - **listnn**: list with the neighbors used for each observation to be predicted - **listd**: list with the distances to the neighbors used for each observation to be predicted - **listw**: list with the weights attributed to the neighbors used for each observation to be predicted ## References Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer. ## Examples ```r n <- 30 ; p <- 10 Xtrain <- matrix(rnorm(n * p), ncol = p) ytrain <- rnorm(n) Ytrain <- cbind(ytrain, 100 * ytrain) m <- 4 Xtest <- matrix(rnorm(m * p), ncol = p) ytest <- rnorm(m) Ytest <- cbind(ytest, 10 * ytest) nlvdis <- 5 ; diss <- "mahal" h <- 2 ; k <- 10 fm <- knnr( Xtrain, Ytrain, nlvdis = nlvdis, diss = diss, h = h, k = k) res <- predict(fm, Xtest) names(res) res$pred msep(res$pred, Ytest) ```

knnr function