# Heteroscedastic discriminant analysis Computes linear transformation of new data into lower dimensional discriminative space using some model produced by `hda`. ```r ## S3 method for class 'hda' predict(object, newdata, alldims = FALSE, task = c("dr", "c"), ...) ``` ## Arguments - `object`: Model resulting from a call of `hda`. - `newdata`: A matrix or data frame to be transformed into lower dimensional space of the same dimension as the data used for building the model. - `alldims`: Logical flag specifying whether the result should contain only the reduced space (default) or should also include the redundant dimensions and thus be of the same dimension as the input data. In this case the reduced space is given by the first `newdim` columns. - `task`: `"dr"` for standard application of the `hda` model to `newdata`. Choose `"c"` for classification of new data. This is an interface to predict function of `naiveBayes`. The option can be chosen if `crule = TRUE` has been specified in the `hda()` call. - ``...``: Further arguments to be passed to the `naiveBayes` predict function. ## Returns If option `type = "dr"` the transformed data are returned. For `type = "c"` both the transformed data as well as the resulting object of the naive Bayes prediction are returned. ## References Kumar, N. and Andreou, A. (1998): **Heteroscedastic discriminant analysis and reduced rank HMMs for improved speech recognition.** Speech Communication 25, pp. 283-297. Szepannek G., Harczos, T., Klefenz, F. and Weihs, C. (2009): **Extending features for automatic speech recognition by means of auditory modelling.** In: Proceedings of European Signal Processing Conference (EUSIPCO) 2009, Glasgow, pp. 1235-1239. ## Author(s) Gero Szepannek ## See Also `hda`, `showloadings`, `plot.hda` ## Examples ```r library(mvtnorm) library(MASS) # simulate data for two classes n <- 50 meana <- meanb <- c(0,0,0,0,0) cova <- diag(5) cova[1,1] <- 0.2 for(i in 3:4){ for(j in (i+1):5){cova[i,j] <- cova[j,i] <- 0.75^(j-i)} } covb <- cova diag(covb)[1:2] <- c(1,0.2) xa <- rmvnorm(n,meana,cova) xb <- rmvnorm(n,meanb,covb) x <- rbind(xa,xb) classes <- as.factor(c(rep(1,n),rep(2,n))) # rotate simulated data symmat <- matrix(runif(5^2),5) symmat <- symmat + t(symmat) even <- eigen(symmat)$vectors rotatedspace <- x %*% even # apply heteroscedastic discriminant analysis and plot data in discriminant space hda.res <- hda(rotatedspace, classes) # simulate new data xanew <- rmvnorm(n,meana,cova) xbnew <- rmvnorm(n,meanb,covb) xnew <- rbind(xanew,xbnew) classes <- as.factor(c(rep(1,n),rep(2,n))) newrotateddata <- x %*% even plot(as.data.frame(newrotateddata), col = classes) # transform new data prediction <- predict(hda.res, newrotateddata) plot(as.data.frame(prediction), col = classes) # predict classes for new data on automatically computed naive Bayes classification rule # this requires package e1071 hda.res2 <- hda(rotatedspace, classes, crule = TRUE) prediction2 <- predict(hda.res2, newrotateddata, task = "c") prediction2 ```

predict.hda function