161 lines
7.3 KiB
R
161 lines
7.3 KiB
R
library(tensorPredictors)
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suppressPackageStartupMessages({
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library(parallel)
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library(pROC)
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})
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#' Mode-Wise PCA preprocessing (generalized (2D)^2 PCA)
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#'
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#' @param npc_time Number of Principal Components for time axis
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#' @param npc_sensor Number of Principal Components for sensor axis
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#' @param npc_condition Number of Principal Components for stimulus condition axis
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preprocess <- function(X, npc_time, npc_sensor, npc_condition) {
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# Mode covariances (for predictor and time point modes)
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c(Sigma_t, Sigma_s, Sigma_c) %<-% mcov(X)
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# "predictor" (sensor) and time point principal components
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V_t <- svd(Sigma_t, npc_time, 0L)$u
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V_s <- svd(Sigma_s, npc_sensor, 0L)$u
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V_c <- svd(Sigma_c, npc_condition, 0L)$u
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# reduce with mode wise PCs
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mlm(X, list(V_t, V_s, V_c), modes = 1:3, transposed = TRUE)
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}
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### Classification performance measures
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# acc: Accuracy. P(Yhat = Y). Estimated as: (TP+TN)/(P+N).
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acc <- function(y.true, y.pred) mean(round(y.pred) == y.true)
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# err: Error rate. P(Yhat != Y). Estimated as: (FP+FN)/(P+N).
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err <- function(y.true, y.pred) mean(round(y.pred) != y.true)
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# fpr: False positive rate. P(Yhat = + | Y = -). aliases: Fallout.
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fpr <- function(y.true, y.pred) mean((round(y.pred) == 1)[y.true == 0])
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# tpr: True positive rate. P(Yhat = + | Y = +). aliases: Sensitivity, Recall.
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tpr <- function(y.true, y.pred) mean((round(y.pred) == 1)[y.true == 1])
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# fnr: False negative rate. P(Yhat = - | Y = +). aliases: Miss.
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fnr <- function(y.true, y.pred) mean((round(y.pred) == 0)[y.true == 1])
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# tnr: True negative rate. P(Yhat = - | Y = -).
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tnr <- function(y.true, y.pred) mean((round(y.pred) == 0)[y.true == 0])
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# auc: Area Under the Curve
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auc <- function(y.true, y.pred) {
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as.numeric(pROC::roc(y.true, y.pred, quiet = TRUE, direction = "<")$auc)
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}
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auc.sd <- function(y.true, y.pred) {
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sqrt(pROC::var(pROC::roc(y.true, y.pred, quiet = TRUE, direction = "<")))
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}
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#' Leave-one-out prediction using TSIR
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#'
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#' @param method reduction method to be applied
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#' @param X 3D EEG data (preprocessed or not)
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#' @param y binary responce vector
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#' @param ... additional arguments passed on to `method`
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loo.predict <- function(method, X, y, ...) {
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# get method function name as character string for logging
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method.name <- as.character(substitute(method))
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# Parallel Leave-One-Out prediction
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unlist(parallel::mclapply(seq_along(y), function(i) {
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# Fit with i'th observation removed
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fit <- method(X[ , , , -i], y[-i], sample.axis = 4L, ...)
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# Reduce the entire data set
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r <- as.vector(mlm(X, fit$betas, modes = 1:3, transpose = TRUE))
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# Fit a logit model on reduced data with i'th observation removed
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logit <- glm(y ~ r, family = binomial(link = "logit"),
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data = data.frame(y = y[-i], r = r[-i])
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)
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# predict i'th response given i'th reduced observation
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y.hat <- predict(logit, newdata = data.frame(r = r[i]), type = "response")
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# report progress
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cat(sprintf("%s - dim: (%d, %d, %d) - %3d/%d\n",
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method.name, dim(X)[1], dim(X)[2], dim(X)[3], i, length(y)
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))
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y.hat
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}, mc.cores = getOption("mc.cores", max(1L, parallel::detectCores() - 1L))))
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}
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# "Projects" a sequence to its first `nr.freq` frequency components
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proj.fft <- function(sequence, nr.freq = 5L) {
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F <- fft(sequence)
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Re(fft(`[<-`(F, head(order(abs(F)), -nr.freq), 0+0i), inverse = TRUE)) / length(F)
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}
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# Load full EEG dataset (3D tensor for each subject)
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c(X, y) %<-% readRDS("eeg_data_3d.rds")
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##################################### GMLM #####################################
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# perform preprocessed (reduced) and raw (not reduced) leave-one-out prediction
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y.hat.3.4 <- loo.predict(gmlm_tensor_normal, preprocess(X, 3, 4, 3), y)
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y.hat.15.15 <- loo.predict(gmlm_tensor_normal, preprocess(X, 15, 15, 3), y)
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y.hat.20.30 <- loo.predict(gmlm_tensor_normal, preprocess(X, 20, 30, 3), y)
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y.hat <- loo.predict(gmlm_tensor_normal, X, y)
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y.hat.fft <- loo.predict(gmlm_tensor_normal, X, y, proj.betas = list(proj.fft, NULL, NULL))
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# classification performance measures table by leave-one-out cross-validation
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(loo.cv <- apply(cbind(y.hat.3.4, y.hat.15.15, y.hat.20.30, y.hat, y.hat.fft), 2, function(y.pred) {
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sapply(c("acc", "err", "fpr", "tpr", "fnr", "tnr", "auc", "auc.sd"),
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function(FUN) { match.fun(FUN)(as.integer(y) - 1L, y.pred) })
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}))
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#> y.hat.3.4 y.hat.15.15 y.hat.20.30 y.hat y.hat.fft
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#> acc 0.83606557 0.80327869 0.80327869 0.79508197 0.79508197
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#> err 0.16393443 0.19672131 0.19672131 0.20491803 0.20491803
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#> fpr 0.31111111 0.33333333 0.33333333 0.35555556 0.33333333
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#> tpr 0.92207792 0.88311688 0.88311688 0.88311688 0.87012987
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#> fnr 0.07792208 0.11688312 0.11688312 0.11688312 0.12987013
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#> tnr 0.68888889 0.66666667 0.66666667 0.64444444 0.66666667
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#> auc 0.88051948 0.86984127 0.86926407 0.86810967 0.86810967
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#> auc.sd 0.03118211 0.03254642 0.03259186 0.03295883 0.03354029
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################################## Tensor SIR ##################################
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# perform preprocessed (reduced) and raw (not reduced) leave-one-out prediction
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y.hat.3.4 <- loo.predict(TSIR, preprocess(X, 3, 4, 3), y)
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y.hat.15.15 <- loo.predict(TSIR, preprocess(X, 15, 15, 3), y)
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y.hat.20.30 <- loo.predict(TSIR, preprocess(X, 20, 30, 3), y)
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y.hat <- loo.predict(TSIR, X, y)
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# classification performance measures table by leave-one-out cross-validation
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(loo.cv <- apply(cbind(y.hat.3.4, y.hat.15.15, y.hat.20.30, y.hat), 2, function(y.pred) {
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sapply(c("acc", "err", "fpr", "tpr", "fnr", "tnr", "auc", "auc.sd"),
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function(FUN) { match.fun(FUN)(as.integer(y) - 1L, y.pred) })
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}))
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#> y.hat.3.4 y.hat.15.15 y.hat.20.30 y.hat
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#> acc 0.81967213 0.84426230 0.81147541 0.80327869
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#> err 0.18032787 0.15573770 0.18852459 0.19672131
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#> fpr 0.33333333 0.24444444 0.33333333 0.33333333
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#> tpr 0.90909091 0.89610390 0.89610390 0.88311688
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#> fnr 0.09090909 0.10389610 0.10389610 0.11688312
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#> tnr 0.66666667 0.75555556 0.66666667 0.66666667
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#> auc 0.86522367 0.89379509 0.88196248 0.85974026
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#> auc.sd 0.03357539 0.03055047 0.02986038 0.03367847
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# perform preprocessed (reduced) and raw (not reduced) leave-one-out prediction
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y.hat.3.4 <- loo.predict(TSIR, preprocess(X, 3, 4, 3), y, cond.threshold = 25)
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y.hat.15.15 <- loo.predict(TSIR, preprocess(X, 15, 15, 3), y, cond.threshold = 25)
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y.hat.20.30 <- loo.predict(TSIR, preprocess(X, 20, 30, 3), y, cond.threshold = 25)
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y.hat <- loo.predict(TSIR, X, y, cond.threshold = 25)
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# classification performance measures table by leave-one-out cross-validation
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(loo.cv <- apply(cbind(y.hat.3.4, y.hat.15.15, y.hat.20.30, y.hat), 2, function(y.pred) {
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sapply(c("acc", "err", "fpr", "tpr", "fnr", "tnr", "auc", "auc.sd"),
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function(FUN) { match.fun(FUN)(as.integer(y) - 1L, y.pred) })
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}))
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#> y.hat.3.4 y.hat.15.15 y.hat.20.30 y.hat
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#> acc 0.81967213 0.77049180 0.76229508 0.77049180
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#> err 0.18032787 0.22950820 0.23770492 0.22950820
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#> fpr 0.33333333 0.37777778 0.40000000 0.37777778
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#> tpr 0.90909091 0.85714286 0.85714286 0.85714286
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#> fnr 0.09090909 0.14285714 0.14285714 0.14285714
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#> tnr 0.66666667 0.62222222 0.60000000 0.62222222
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#> auc 0.86522367 0.84386724 0.84415584 0.84040404
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#> auc.sd 0.03357539 0.03542706 0.03519592 0.03558135
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