Software companion for the paper “Localization processes for functional data analysis” by Elías, Antonio, Jiménez, Raúl, and Yukich, Joe, (2020) <arXiv:2007.16059>. It provides the code for computing localization processes and localization distances and their application to classification and outlier detection problems.
#install the package
devtools::install_github("aefdz/localFDA")## v checking for file 'C:\Users\anton\AppData\Local\Temp\Rtmp4617Sq\remotes2e00503a197c\aefdz-localFDA-25b0d40/DESCRIPTION' (425ms)
## - preparing 'localFDA':
## checking DESCRIPTION meta-information ... checking DESCRIPTION meta-information ... v checking DESCRIPTION meta-information
## - checking for LF line-endings in source and make files and shell scripts
## - checking for empty or unneeded directories
## - looking to see if a 'data/datalist' file should be added
## - building 'localFDA_0.0.0.9000.tar.gz'
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#load the package
library(localFDA)Load the example data and plot it.
X <- exampleData
n <- ncol(X)
p <- nrow(X)
t <- as.numeric(rownames(X))
#plot the data set
df_functions <- data.frame(ids = rep(colnames(X), each = p),
y = c(X),
x = rep(t, n)
)
functions_plot <- ggplot(df_functions) +
geom_line(aes(x = x, y = y, group = ids, color = ids),
color = "black", alpha = 0.25) +
xlab("t") + theme(legend.position = "none")
functions_plot
Empirical version of Equation (1) of the paper. For one focal,
focal <- "1"
localizarionProcesses_focal <- localizationProcesses(X, focal)$lcPlot localization processes of order 1, 50, 100 and 200:
df_lc <- data.frame(k = rep(colnames(localizarionProcesses_focal), each = p),
y = c(localizarionProcesses_focal),
x = rep(t, n-1)
)
lc_plots <- list()
ks <- c(1, 50, 100, 200)
for(i in 1:4){
lc_plots[[i]] <- functions_plot +
geom_line(data = filter(df_lc, k == paste0("k=", ks[i])),
aes(x = x, y = y, group = k),
color = "blue", size = 1) +
geom_line(data = filter(df_functions, ids == focal),
aes(x = x, y = y, group = ids),
color = "red", linetype = "dashed", size = 1)+
ggtitle(paste("k = ", ks[i]))
}
wrap_plots(lc_plots)
Equation (18) of the paper. For one focal,
localizationDistances_focal <- localizationDistances(X, focal)
head(localizationDistances_focal)## k=1 k=2 k=3 k=4 k=5 k=6
## 0.0005082926 0.0011346495 0.0017636690 0.0023955745 0.0030095117 0.0035089220
Plot the localization distances:
df_ld <- data.frame(k = names(localizationDistances_focal),
y = localizationDistances_focal,
x = 1:c(n-1)
)
ldistances_plot <- ggplot(df_ld, aes(x = x, y = y)) +
geom_point() +
ggtitle("Localization distances for one focal") +
xlab("kth") + ylab("L")
ldistances_plot
localizationStatistics_full <- localizationStatistics(X, robustify = TRUE)
#See the mean and sd estimations for k = 1, 100, 200, 400, 600
localizationStatistics_full$trim_mean[c(1, 100, 200, 400, 600)]## k=1 k=100 k=200 k=400 k=600
## 0.001083517 0.098465426 0.184940365 0.350528860 0.526580274
localizationStatistics_full$trim_sd[c(1, 100, 200, 400, 600)]## k=1 k=100 k=200 k=400 k=600
## 0.0005326429 0.0329170846 0.0490732397 0.0686018224 0.0806314699
X <- classificationData
ids_training <- sample(colnames(X), 90)
ids_testing <- setdiff(colnames(X), ids_training)
trainingSample <- X[,ids_training]
testSample <- X[,ids_testing]; colnames(testSample) <- NULL #blind
classNames <- c("G1", "G2")
classification_results <- localizationClassifier(trainingSample, testSample, classNames, k_opt = 3)
checking <- data.frame(real_classs = ids_testing,
predicted_class =classification_results$test$predicted_class)
checking## real_classs predicted_class
## 1 12_G1 G1
## 2 14_G1 G1
## 3 21_G1 G1
## 4 44_G1 G1
## 5 54_G2 G2
## 6 56_G2 G2
## 7 72_G2 G2
## 8 81_G2 G2
## 9 94_G2 G2
## 10 100_G2 G2
X <- outlierData
outliers <- outlierLocalizationDistance(X, localrule = 0.95, whiskerrule = 1.5)
outliers$outliers_ld_rule## [1] "1_magnitude" "1_shape" "2_magnitude" "2_shape"
Plot results,
df_functions <- data.frame(ids = rep(colnames(X), each = nrow(X)),
y = c(X),
x = rep(seq(from = 0, to = 1, length.out = nrow(X)), ncol(X)))
functions_plot <- ggplot(df_functions) +
geom_line(aes(x = x, y = y, group = ids),
color = "black") +
xlab("t") +
theme(legend.position = "bottom")+
geom_line(data = df_functions[df_functions$ids %in% outliers$outliers_ld_rule,], aes(x = x, y = y, group = ids, color = ids), size = 1) +
guides(color = guide_legend(title="Detected outliers"))
functions_plot 
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis [https://arxiv.org/abs/2007.16059]https://arxiv.org/abs/2007.16059.
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