| Title: | Localization Processes for Functional Data Analysis |
|---|---|
| Description: | Implementation of a theoretically supported alternative to k-nearest neighbors for functional data to solve problems of estimating unobserved segments of a partially observed functional data sample, functional classification and outlier detection. The approximating neighbor curves are piecewise functions built from a functional sample. Instead of a distance on a function space we use a locally defined distance function that satisfies stabilization criteria. The package allows the implementation of the methodology and the replication of the results in Elías, A., Jiménez, R. and Yukich, J. (2020) <arXiv:2007.16059>. |
| Authors: | Antonio Elías [aut, cre], Raul Jiménez [aut], Joe Yukich [aut] |
| Maintainer: | Antonio Elías <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.0 |
| Built: | 2025-01-30 05:37:25 UTC |
| Source: | https://github.com/aefdz/localfda |
Two groups of Gaussian processes with different mean values
classificationDataclassificationData
A matrix with n = 100 functions by columns and t = 200 evaluation points by row. The first 50 are G1 and second 50 curves are G2 that differs in the mean value.
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
matplot(classificationData, type = "l")matplot(classificationData, type = "l")
Functional Gaussian processes.
exampleDataexampleData
A matrix with n = 1000 functions by columns and t = 100 evaluation points by row.
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
matplot(exampleData, type = "l")matplot(exampleData, type = "l")
Given a training sample with g groups, it predicts the group of the test sample.
localizationClassifier(trainingSample, testSample, classNames, k_opt, g_pi)localizationClassifier(trainingSample, testSample, classNames, k_opt, g_pi)
trainingSample |
matrix p by n, being n the number of functions and p the number of grid points. The colnames of the trainingSample matrix are i_groupName where i goes from 1 to the sample size of the group. |
testSample |
matrix p by n, being n the number of functions to classify and p the number of grid points. |
classNames |
character vector with the group names. |
k_opt |
Maximum order of the localization processes used in the classification rule. |
g_pi |
Vector of size g with a priori probabilities for the bayes classifier. If it is missing the probability is defined by the proportion of curves of each group. |
Two named training and test. Training contains the estimations made with the training sample (localization statistics and localization distances). Test contains the classification results (for each incoming data, localization distances in each group, prior probabilities used, likelihood in each group and the predicted_class).
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
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)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)
Compute the localization distances of order k of the curve y0.
localizationDistances(y, y0)localizationDistances(y, y0)
y |
matrix p by n, being n the number of functions and p the number of grid points. |
y0 |
focal curve (index or character name). |
a vector of length (n-1), being the localization distance of its corresponding order.
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
localizationDistances_1 <- localizationDistances(exampleData, y0 = "1")localizationDistances_1 <- localizationDistances(exampleData, y0 = "1")
Compute the localization processes of order k of the curve y0.
localizationProcesses(y, y0)localizationProcesses(y, y0)
y |
matrix p by n, being n the number of functions and p the number of grid points. |
y0 |
focal curve index or name |
a list with one element, lc, a matrix of size p x (n-1), being the (n-1) columns the localization processes of its corresponding order.
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
localizationProcesses_1 <- localizationProcesses(exampleData, y0 = "1")localizationProcesses_1 <- localizationProcesses(exampleData, y0 = "1")
Estimate the mean and standard deviation of the localization distances mean.
localizationStatistics(y, robustify = TRUE, whiskerrule)localizationStatistics(y, robustify = TRUE, whiskerrule)
y |
matrix p by n, being n the number of functions and p the number of grid points. |
robustify |
if TRUE the mean and standard deviation are estimated with a the trimmed sample. Default is TRUE. |
whiskerrule |
Range parameter for the univariate boxplot detection rule. Default = 3. |
a list with the localization distances of each function (localizationDistances), the estimated mean (mean) and standard deviation (sd).
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
localizationStatistics_full <- localizationStatistics(exampleData[,1:101], robustify = TRUE) localizationStatistics_full$trim_mean[c(1, 25, 50 ,75, 100)] localizationStatistics_full$trim_sd[c(1, 25, 50 ,75, 100)]localizationStatistics_full <- localizationStatistics(exampleData[,1:101], robustify = TRUE) localizationStatistics_full$trim_mean[c(1, 25, 50 ,75, 100)] localizationStatistics_full$trim_sd[c(1, 25, 50 ,75, 100)]
Functional Gaussian processes with outliers.
outlierDataoutlierData
A matrix with n = 54 functions by columns and t = 200 evaluation points by row. The last 4 observations are two shape and two magnitude outliers.
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
matplot(outlierData, type = "l")matplot(outlierData, type = "l")
Compute the localization distances of order k of the curve y0.
outlierLocalizationDistance(X, localrule = 0.9, whiskerrule = 3)outlierLocalizationDistance(X, localrule = 0.9, whiskerrule = 3)
X |
matrix p by n, being n the number of functions and p the number of grid points. |
localrule |
Local distance rule: the method marks a curve as outlier if its k order localization distances are outliers in more than local_rulex100 percent of the k-order univariate boxplots. Default is 0.90 so a function must be at least an outlier in 90 percent of the k-order localization distances. |
whiskerrule |
Parameter for the whiskers of the univariate boxplot of the localization distances of order kth. Default value is 3. |
A list
Elías, Antonio, Jiménez, Raúl and Yukich, Joe (2020). Localization processes for functional data analysis (submitted).
outliers <- outlierLocalizationDistance(outlierData, localrule = 0.9, whiskerrule = 3) outliers$outliers_ld_ruleoutliers <- outlierLocalizationDistance(outlierData, localrule = 0.9, whiskerrule = 3) outliers$outliers_ld_rule