| Type: | Package |
| Title: | Archetypoid Algorithms and Anomaly Detection |
| Version: | 1.2.1 |
| Date: | 2020-08-04 |
| Author: | Guillermo Vinue, Irene Epifanio |
| Maintainer: | Guillermo Vinue <Guillermo.Vinue@uv.es> |
| Description: | Collection of several algorithms to obtain archetypoids with small and large databases, and with both classical multivariate data and functional data (univariate and multivariate). Some of these algorithms also allow to detect anomalies (outliers). Please see Vinue and Epifanio (2020) <doi:10.1007/s11634-020-00412-9>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://www.r-project.org |
| Depends: | R (≥ 3.4.0) |
| Imports: | Anthropometry, archetypes, FNN, foreach, graphics, nnls, parallel, stats, tolerance, univOutl, utils |
| Suggests: | doParallel, fda |
| LazyData: | true |
| RoxygenNote: | 6.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2020-08-04 09:51:01 UTC; guillevinue |
| Repository: | CRAN |
| Date/Publication: | 2020-08-04 12:30:14 UTC |
Multivariate parallel archetypoid algorithm for large applications (ADALARA)
Description
The ADALARA algorithm is based on the CLARA clustering algorithm. This is the parallel version of the algorithm to try to get faster results. It allows to detect anomalies (outliers). There are two different methods to detect them: the adjusted boxplot (default and most reliable option) and tolerance intervals. If needed, tolerance intervals allow to define a degree of outlierness.
Usage
adalara(data, N, m, numArchoid, numRep, huge, prob, type_alg = "ada",
compare = FALSE, vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox", frame)
Arguments
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. The data must have row names so that the algorithm can identify the archetypoids in every sample. |
N |
Number of samples. |
m |
Sample size of each sample. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
type_alg |
String. Options are 'ada' for the non-robust adalara algorithm and 'ada_rob' for the robust adalara algorithm. |
compare |
Boolean argument to compute the robust residual sum of squares
if |
vect_tol |
Vector with the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
frame |
Boolean value to indicate whether the frame is computed (Mair et al., 2017) or not. The frame is made up of a subset of extreme points, so the archetypoids are only computed on the frame. Low frame densities are obtained when only small portions of the data were extreme. However, high frame densities reduce this speed-up. |
Value
A list with the following elements:
cases Optimal vector of archetypoids.
rss Optimal residual sum of squares.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Hubert, M. and Vandervieren, E., An adjusted boxplot for skewed distributions, 2008. Computational Statistics and Data Analysis 52(12), 5186-5201, https://doi.org/10.1016/j.csda.2007.11.008
Kaufman, L. and Rousseeuw, P.J., Clustering Large Data Sets, 1986. Pattern Recognition in Practice, 425-437.
Mair, S., Boubekki, A. and Brefeld, U., Frame-based Data Factorizations, 2017. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, 1-9.
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
See Also
do_ada, do_ada_robust, adalara_no_paral
Examples
## Not run:
library(Anthropometry)
library(doParallel)
# Prepare parallelization (including the seed for reproducibility):
no_cores <- detectCores() - 1
cl <- makeCluster(no_cores)
registerDoParallel(cl)
clusterSetRNGStream(cl, iseed = 1)
# Load data:
data(mtcars)
data <- mtcars
n <- nrow(data)
# Arguments for the archetype/archetypoid algorithm:
# Number of archetypoids:
k <- 3
numRep <- 2
huge <- 200
# Size of the random sample of observations:
m <- 10
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
# ADALARA algorithm:
preproc <- preprocessing(data, stand = TRUE, percAccomm = 1)
data1 <- as.data.frame(preproc$data)
adalara_aux <- adalara(data1, N, m, k, numRep, huge, prob,
"ada_rob", FALSE, method = "adjbox", frame = FALSE)
#adalara_aux <- adalara(data1, N, m, k, numRep, huge, prob,
# "ada_rob", FALSE, vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
# outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
# method = "toler", frame = FALSE)
# Take the minimum RSS, which is in the second position of every sublist:
adalara <- adalara_aux[which.min(unlist(sapply(adalara_aux, function(x) x[2])))][[1]]
adalara
# End parallelization:
stopCluster(cl)
## End(Not run)
Multivariate non-parallel archetypoid algorithm for large applications (ADALARA)
Description
The ADALARA algorithm is based on the CLARA clustering algorithm. This is the non-parallel version of the algorithm. It allows to detect anomalies (outliers). There are two different methods to detect them: the adjusted boxplot (default and most reliable option) and tolerance intervals. If needed, tolerance intervals allow to define a degree of outlierness.
Usage
adalara_no_paral(data, seed, N, m, numArchoid, numRep, huge, prob, type_alg = "ada",
compare = FALSE, verbose = TRUE, vect_tol = c(0.95, 0.9, 0.85),
alpha = 0.05, outl_degree = c("outl_strong", "outl_semi_strong",
"outl_moderate"), method = "adjbox", frame)
Arguments
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. The data must have row names so that the algorithm can identify the archetypoids in every sample. |
seed |
Integer value to set the seed. This ensures reproducibility. |
N |
Number of samples. |
m |
Sample size of each sample. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
type_alg |
String. Options are 'ada' for the non-robust adalara algorithm and 'ada_rob' for the robust adalara algorithm. |
compare |
Boolean argument to compute the robust residual sum of squares
if |
verbose |
Display progress? Default TRUE. |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
frame |
Boolean value to indicate whether the frame is computed (Mair et al., 2017) or not. The frame is made up of a subset of extreme points, so the archetypoids are only computed on the frame. Low frame densities are obtained when only small portions of the data were extreme. However, high frame densities reduce this speed-up. |
Value
A list with the following elements:
cases Optimal vector of archetypoids.
rss Optimal residual sum of squares.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Hubert, M. and Vandervieren, E., An adjusted boxplot for skewed distributions, 2008. Computational Statistics and Data Analysis 52(12), 5186-5201, https://doi.org/10.1016/j.csda.2007.11.008
Kaufman, L. and Rousseeuw, P.J., Clustering Large Data Sets, 1986. Pattern Recognition in Practice, 425-437.
Mair, S., Boubekki, A. and Brefeld, U., Frame-based Data Factorizations, 2017. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, 1-9.
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
See Also
do_ada, do_ada_robust, adalara
Examples
## Not run:
library(Anthropometry)
# Load data:
data(mtcars)
data <- mtcars
n <- nrow(data)
# Arguments for the archetype/archetypoid algorithm:
# Number of archetypoids:
k <- 3
numRep <- 2
huge <- 200
# Size of the random sample of observations:
m <- 10
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
# ADALARA algorithm:
preproc <- preprocessing(data, stand = TRUE, percAccomm = 1)
data1 <- as.data.frame(preproc$data)
res_adalara <- adalara_no_paral(data1, 1, N, m, k,
numRep, huge, prob, "ada_rob", FALSE, TRUE,
method = "adjbox", frame = FALSE)
# Examine the results:
res_adalara
res_adalara1 <- adalara_no_paral(data1, 1, N, m, k,
numRep, huge, prob, "ada_rob", FALSE, TRUE,
vect_tol = c(0.95, 0.9, 0.85),
alpha = 0.05, outl_degree = c("outl_strong", "outl_semi_strong",
"outl_moderate"),
method = "toler", frame = FALSE)
res_adalara1
## End(Not run)
Archetypoid algorithm with the functional Frobenius norm
Description
Archetypoid algorithm with the functional Frobenius norm to be used with functional data.
Usage
archetypoids_funct(numArchoid, data, huge = 200, ArchObj, PM)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
PM |
Penalty matrix obtained with |
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
lass <- stepArchetypesRawData_funct(data = data_archs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM)
af <- archetypoids_funct(3, data_archs, huge = 200, ArchObj = lass, PM)
str(af)
## End(Not run)
Archetypoid algorithm with the functional multivariate Frobenius norm
Description
Archetypoid algorithm with the functional multivariate Frobenius norm to be used with functional data.
Usage
archetypoids_funct_multiv(numArchoid, data, huge = 200, ArchObj, PM)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
PM |
Penalty matrix obtained with |
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
lass <- stepArchetypesRawData_funct_multiv(data = Xs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM)
afm <- archetypoids_funct_multiv(3, Xs, huge = 200, ArchObj = lass, PM)
str(afm)
## End(Not run)
Archetypoid algorithm with the functional multivariate robust Frobenius norm
Description
Archetypoid algorithm with the functional multivariate robust Frobenius norm to be used with functional data.
Usage
archetypoids_funct_multiv_robust(numArchoid, data, huge = 200, ArchObj, PM, prob)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
lass <- stepArchetypesRawData_funct_multiv_robust(data = Xs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM, prob = 0.8,
nbasis, nvars)
afmr <- archetypoids_funct_multiv_robust(3, Xs, huge = 200, ArchObj = lass, PM, 0.8)
str(afmr)
## End(Not run)
Archetypoid algorithm with the functional robust Frobenius norm
Description
Archetypoid algorithm with the functional robust Frobenius norm to be used with functional data.
Usage
archetypoids_funct_robust(numArchoid, data, huge = 200, ArchObj, PM, prob)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
lass <- stepArchetypesRawData_funct_robust(data = data_archs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM, prob = 0.8)
afr <- archetypoids_funct_robust(3, data_archs, huge = 200, ArchObj = lass, PM, 0.8)
str(afr)
## End(Not run)
Archetypoid algorithm with the Frobenius norm
Description
This function is the same as archetypoids but the 2-norm
is replaced by the Frobenius norm. Thus, the comparison with the robust archetypoids
can be directly made.
Usage
archetypoids_norm_frob(numArchoid, data, huge = 200, ArchObj)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Vinue, G., Epifanio, I., and Alemany, S., Archetypoids: a new approach to define representative archetypal data, 2015. Computational Statistics and Data Analysis 87, 102-115, https://doi.org/10.1016/j.csda.2015.01.018
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
See Also
Examples
data(mtcars)
data <- mtcars
k <- 3
numRep <- 2
huge <- 200
lass <- stepArchetypesRawData_norm_frob(data = data, numArch = k,
numRep = numRep, verbose = FALSE)
res <- archetypoids_norm_frob(k, data, huge, ArchObj = lass)
str(res)
res$cases
res$rss
Archetypoid algorithm with the robust Frobenius norm
Description
Robust version of the archetypoid algorithm with the Frobenius form.
Usage
archetypoids_robust(numArchoid, data, huge = 200, ArchObj, prob)
Arguments
numArchoid |
Number of archetypoids. |
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. |
huge |
Penalization added to solve the convex least squares problems. |
ArchObj |
The list object returned by the
|
prob |
Probability with values in [0,1]. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
archet_ini: Vector of initial archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
resid: Matrix with the residuals.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
Examples
data(mtcars)
data <- mtcars
k <- 3
numRep <- 2
huge <- 200
lass <- stepArchetypesRawData_robust(data = data, numArch = k,
numRep = numRep, verbose = FALSE,
saveHistory = FALSE, prob = 0.8)
res <- archetypoids_robust(k, data, huge, ArchObj = lass, 0.8)
str(res)
res$cases
res$rss
Bisquare function
Description
This function belongs to the bisquare family of loss functions. The bisquare family can better cope with extreme outliers.
Usage
bisquare_function(resid, prob, ...)
Arguments
resid |
Vector of residuals, computed from the
|
prob |
Probability with values in [0,1]. |
... |
Additional possible arguments. |
Value
Vector of real numbers.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
resid <- c(2.47, 11.85)
bisquare_function(resid, 0.8)
Run the whole classical archetypoid analysis with the Frobenius norm
Description
This function executes the entire procedure involved in the archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the archetypal algorithm and finally, the optimal vector of archetypoids is returned.
Usage
do_ada(subset, numArchoid, numRep, huge, compare = FALSE,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox", prob)
Arguments
subset |
Data to obtain archetypes. In ADALARA this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
compare |
Boolean argument to compute the robust residual sum of squares
to compare these results with the ones provided by |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
prob |
If |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_rob: If
compare=TRUE, this is the residual sum of squares using the robust Frobenius norm. Otherwise, NULL.resid: Vector with the residuals.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Vinue, G., Epifanio, I., and Alemany, S., Archetypoids: a new approach to define representative archetypal data, 2015. Computational Statistics and Data Analysis 87, 102-115, https://doi.org/10.1016/j.csda.2015.01.018
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
See Also
stepArchetypesRawData_norm_frob, archetypoids_norm_frob
Examples
library(Anthropometry)
data(mtcars)
#data <- as.matrix(mtcars)
data <- mtcars
k <- 3
numRep <- 2
huge <- 200
preproc <- preprocessing(data, stand = TRUE, percAccomm = 1)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_ada <- do_ada(preproc$data, k, numRep, huge, FALSE, method = "adjbox")
str(res_ada)
res_ada1 <- do_ada(preproc$data, k, numRep, huge, FALSE,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong",
"outl_moderate"), method = "toler")
str(res_ada1)
res_ada2 <- do_ada(preproc$data, k, numRep, huge, TRUE, method = "adjbox", prob = 0.8)
str(res_ada2)
Run the whole robust archetypoid analysis with the robust Frobenius norm
Description
This function executes the entire procedure involved in the robust archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the robust archetypal algorithm and finally, the optimal vector of robust archetypoids is returned.
Usage
do_ada_robust(subset, numArchoid, numRep, huge, prob, compare = FALSE,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox")
Arguments
subset |
Data to obtain archetypes. In ADALARA this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
compare |
Boolean argument to compute the non-robust residual sum of squares
to compare these results with the ones provided by |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_non_rob: If
compare=TRUE, this is the residual sum of squares using the non-robust Frobenius norm. Otherwise, NULL.resid Vector of residuals.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
stepArchetypesRawData_robust, archetypoids_robust
Examples
## Not run:
library(Anthropometry)
data(mtcars)
#data <- as.matrix(mtcars)
data <- mtcars
k <- 3
numRep <- 2
huge <- 200
preproc <- preprocessing(data, stand = TRUE, percAccomm = 1)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_ada_rob <- do_ada_robust(preproc$data, k, numRep, huge, 0.8,
FALSE, method = "adjbox")
str(res_ada_rob)
res_ada_rob1 <- do_ada_robust(preproc$data, k, numRep, huge, 0.8,
FALSE, vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong",
"outl_moderate"),
method = "toler")
str(res_ada_rob1)
## End(Not run)
Alphas and RSS of every set of archetypoids
Description
In the ADALARA algorithm, every time that a set of archetypoids is computed using a sample of the data, the alpha coefficients and the associated residual sum of squares (RSS) for the entire data set must be computed.
Usage
do_alphas_rss(data, subset, huge, k_subset, rand_obs, alphas_subset,
type_alg = "ada", PM, prob)
Arguments
data |
Data matrix with all the observations. |
subset |
Data matrix with a sample of the |
huge |
Penalization added to solve the convex least squares problems. |
k_subset |
Archetypoids obtained from |
rand_obs |
Sample observations that form |
alphas_subset |
Alpha coefficients related to |
type_alg |
String. Options are 'ada' for the non-robust multivariate adalara algorithm, 'ada_rob' for the robust multivariate adalara algorithm, 'fada' for the non-robust fda fadalara algorithm and 'fada_rob' for the robust fda fadalara algorithm. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. Needed when
|
Value
A list with the following elements:
rss Real number of the residual sum of squares.
resid_rss Matrix with the residuals.
alphas Matrix with the alpha values.
Author(s)
Guillermo Vinue
See Also
Examples
data(mtcars)
data <- mtcars
n <- nrow(data)
m <- 10
k <- 3
numRep <- 2
huge <- 200
suppressWarnings(RNGversion("3.5.0"))
set.seed(1)
rand_obs_si <- sample(1:n, size = m)
si <- data[rand_obs_si,]
ada_si <- do_ada(si, k, numRep, huge, FALSE)
k_si <- ada_si$cases
alphas_si <- ada_si$alphas
colnames(alphas_si) <- rownames(si)
rss_si <- do_alphas_rss(data, si, huge, k_si, rand_obs_si, alphas_si, "ada")
str(rss_si)
Alphas and RSS of every set of multivariate archetypoids
Description
In the ADALARA algorithm, every time that a set of archetypoids is computed using a sample of the data, the alpha coefficients and the associated residual sum of squares (RSS) for the entire data set must be computed.
Usage
do_alphas_rss_multiv(data, subset, huge, k_subset, rand_obs, alphas_subset,
type_alg = "ada", PM, prob, nbasis, nvars)
Arguments
data |
Data matrix with all the observations. |
subset |
Data matrix with a sample of the |
huge |
Penalization added to solve the convex least squares problems. |
k_subset |
Archetypoids obtained from |
rand_obs |
Sample observations that form |
alphas_subset |
Alpha coefficients related to |
type_alg |
String. Options are 'ada' for the non-robust multivariate adalara algorithm, 'ada_rob' for the robust multivariate adalara algorithm, 'fada' for the non-robust fda fadalara algorithm and 'fada_rob' for the robust fda fadalara algorithm. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. Needed when
|
nbasis |
Number of basis. |
nvars |
Number of variables. |
Value
A list with the following elements:
rss Real number of the residual sum of squares.
resid_rss Matrix with the residuals.
alphas Matrix with the alpha values.
Author(s)
Guillermo Vinue
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
# We have to give names to the dimensions to know the
# observations that were identified as archetypoids.
dimnames(Xs) <- list(paste("Obs", 1:dim(hgtm)[2], sep = ""),
1:nbasis,
c("boys", "girls"))
n <- dim(Xs)[1]
# Number of archetypoids:
k <- 3
numRep <- 20
huge <- 200
# Size of the random sample of observations:
m <- 15
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
data_alg <- Xs
nbasis <- dim(data_alg)[2] # number of basis.
nvars <- dim(data_alg)[3] # number of variables.
n <- nrow(data_alg)
suppressWarnings(RNGversion("3.5.0"))
set.seed(1)
rand_obs_si <- sample(1:n, size = m)
si <- apply(data_alg, 2:3, function(x) x[rand_obs_si])
fada_si <- do_fada_multiv_robust(si, k, numRep, huge, 0.8, FALSE, PM)
k_si <- fada_si$cases
alphas_si <- fada_si$alphas
colnames(alphas_si) <- rownames(si)
rss_si <- do_alphas_rss_multiv(data_alg, si, huge, k_si, rand_obs_si, alphas_si,
"fada_rob", PM, 0.8, nbasis, nvars)
str(rss_si)
## End(Not run)
Cleaning outliers
Description
Cleaning of the most remarkable outliers. This improves the performance of the archetypoid algorithm since it is not affected by spurious points.
Usage
do_clean(data, num_pts, range = 1.5, out_perc = 80)
Arguments
data |
Data frame with (temporal) points in the rows and observations in the columns. |
num_pts |
Number of temporal points. |
range |
Same parameter as in function |
out_perc |
Minimum number of temporal points (in percentage) to consider
the observation as an outlier. Needed when |
Value
Numeric vector with the outliers.
Author(s)
Irene Epifanio
See Also
Examples
data(mtcars)
data <- mtcars
num_pts <- ncol(data)
do_clean(t(data), num_pts, 1.5, 80)
Cleaning multivariate functional outliers
Description
Cleaning of the most remarkable multivariate functional outliers. This improves the performance of the archetypoid algorithm since it is not affected by spurious points.
Usage
do_clean_multiv(data, num_pts, range = 1.5, out_perc = 80, nbasis, nvars)
Arguments
data |
Data frame with (temporal) points in the rows and observations in the columns. |
num_pts |
Number of temporal points. |
range |
Same parameter as in function |
out_perc |
Minimum number of temporal points (in percentage) to consider
the observation as an outlier. Needed when |
nbasis |
Number of basis. |
nvars |
Number of variables. |
Value
List with the outliers for each variable.
Author(s)
Irene Epifanio
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
x1 <- t(Xs[,,1])
for (i in 2:nvars) {
x12 <- t(Xs[,,i])
x1 <- rbind(x1, x12)
}
data_all <- t(x1)
num_pts <- ncol(data_all) / nvars
range <- 3
outl <- do_clean_multiv(t(data_all), num_pts, range, out_perc, nbasis, nvars)
outl
## End(Not run)
Run the whole functional archetypoid analysis with the Frobenius norm
Description
This function executes the entire procedure involved in the functional archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the functional archetypal algorithm and finally, the optimal vector of archetypoids is returned.
Usage
do_fada(subset, numArchoid, numRep, huge, compare = FALSE, PM,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox", prob)
Arguments
subset |
Data to obtain archetypes. In fadalara this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
compare |
Boolean argument to compute the robust residual sum of squares
to compare these results with the ones provided by |
PM |
Penalty matrix obtained with |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
prob |
If |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_rob: If
compare_robust=TRUE, this is the residual sum of squares using the robust Frobenius norm. Otherwise, NULL.resid: Vector of residuals.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
See Also
stepArchetypesRawData_funct, archetypoids_funct
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada <- do_fada(subset = data_archs, numArchoid = 3, numRep = 5, huge = 200,
compare = FALSE, PM = PM, method = "adjbox")
str(res_fada)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada1 <- do_fada(subset = data_archs, numArchoid = 3, numRep = 5, huge = 200,
compare = FALSE, PM = PM,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "toler")
str(res_fada1)
res_fada2 <- do_fada(subset = data_archs, numArchoid = 3, numRep = 5, huge = 200,
compare = TRUE, PM = PM, method = "adjbox", prob = 0.8)
str(res_fada2)
## End(Not run)
Run the whole archetypoid analysis with the functional multivariate Frobenius norm
Description
This function executes the entire procedure involved in the functional archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the functional archetypal algorithm and finally, the optimal vector of archetypoids is returned.
Usage
do_fada_multiv(subset, numArchoid, numRep, huge, compare = FALSE, PM,
method = "adjbox", prob)
Arguments
subset |
Data to obtain archetypes. In fadalara this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
compare |
Boolean argument to compute the robust residual sum of squares
to compare these results with the ones provided by |
PM |
Penalty matrix obtained with |
method |
Method to compute the outliers. So far the only option allowed is 'adjbox' for using adjusted boxplots for skewed distributions. The use of tolerance intervals might also be explored in the future for the multivariate case. |
prob |
If |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_rob: If
compare_robust=TRUE, this is the residual sum of squares using the robust Frobenius norm. Otherwise, NULL.resid: Vector of residuals.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
See Also
stepArchetypesRawData_funct_multiv, archetypoids_funct_multiv
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada <- do_fada_multiv(subset = Xs, numArchoid = 3, numRep = 5, huge = 200,
compare = FALSE, PM = PM, method = "adjbox")
str(res_fada)
## End(Not run)
Run the whole archetypoid analysis with the functional multivariate robust Frobenius norm
Description
This function executes the entire procedure involved in the functional archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the functional archetypal algorithm and finally, the optimal vector of archetypoids is returned.
Usage
do_fada_multiv_robust(subset, numArchoid, numRep, huge, prob, compare = FALSE, PM,
method = "adjbox")
Arguments
subset |
Data to obtain archetypes. In fadalara this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization to solve the convex least squares problem,
see |
prob |
Probability with values in [0,1]. |
compare |
Boolean argument to compute the non-robust residual sum of squares
to compare these results with the ones provided by |
PM |
Penalty matrix obtained with |
method |
Method to compute the outliers. So far the only option allowed is 'adjbox' for using adjusted boxplots for skewed distributions. The use of tolerance intervals might also be explored in the future for the multivariate case. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_non_rob: If
compare=TRUE, this is the residual sum of squares using the non-robust Frobenius norm. Otherwise, NULL.resid Vector of residuals.
outliers: Outliers.
local_rel_imp Matrix with the local (casewise) relative importance (in percentage) of each variable for the outlier identification. Only for the multivariate case. It is relative to the outlier observation itself. The other observations are not considered for computing this importance. This procedure works because the functional variables are in the same scale, after standardizing. Otherwise, it couldn't be interpreted like that.
margi_rel_imp Matrix with the marginal relative importance of each variable (in percentage) for the outlier identification. Only for the multivariate case. In this case, the other points are considered, since the value of the outlier observation is compared with the remaining points.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
stepArchetypesRawData_funct_multiv_robust,
archetypoids_funct_multiv_robust
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada <- do_fada_multiv_robust(subset = Xs, numArchoid = 3, numRep = 5, huge = 200,
prob = 0.75, compare = FALSE, PM = PM, method = "adjbox")
str(res_fada)
res_fada$cases
#[1] 8 24 29
res_fada$rss
#[1] 2.301741
## End(Not run)
Run the whole archetypoid analysis with the functional robust Frobenius norm
Description
This function executes the entire procedure involved in the functional archetypoid analysis. Firstly, the initial vector of archetypoids is obtained using the functional archetypal algorithm and finally, the optimal vector of archetypoids is returned.
Usage
do_fada_robust(subset, numArchoid, numRep, huge, prob, compare = FALSE, PM,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox")
Arguments
subset |
Data to obtain archetypes. In fadalara this is a subset of the entire data frame. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
compare |
Boolean argument to compute the non-robust residual sum of squares
to compare these results with the ones provided by |
PM |
Penalty matrix obtained with |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for using adjusted boxplots for skewed distributions, and 'toler' for using tolerance intervals. |
Value
A list with the following elements:
cases: Final vector of archetypoids.
alphas: Alpha coefficients for the final vector of archetypoids.
rss: Residual sum of squares corresponding to the final vector of archetypoids.
rss_non_rob: If
compare=TRUE, this is the residual sum of squares using the non-robust Frobenius norm. Otherwise, NULL.resid: Vector of residuals.
outliers: Outliers.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
stepArchetypesRawData_funct_robust,
archetypoids_funct_robust
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada_rob <- do_fada_robust(subset = data_archs, numArchoid = 3, numRep = 5, huge = 200,
prob = 0.75, compare = FALSE, PM = PM, method = "adjbox")
str(res_fada_rob)
suppressWarnings(RNGversion("3.5.0"))
set.seed(2018)
res_fada_rob1 <- do_fada_robust(subset = data_archs, numArchoid = 3, numRep = 5, huge = 200,
prob = 0.75, compare = FALSE, PM = PM,
vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "toler")
str(res_fada_rob1)
## End(Not run)
kNN for outlier detection
Description
Ramaswamy et al. proposed the k-nearest neighbors outlier detection method (kNNo). Each point's anomaly score is the distance to its kth nearest neighbor in the data set. Then, all points are ranked based on this distance. The higher an example's score is, the more anomalous it is.
Usage
do_knno(data, k, top_n)
Arguments
data |
Data observations. |
k |
Number of neighbors of a point that we are interested in. |
top_n |
Total number of outliers we are interested in. |
Value
Vector of outliers.
Author(s)
Guillermo Vinue
References
Ramaswamy, S., Rastogi, R. and Shim, K. Efficient Algorithms for Mining Outliers from Large Data Sets. SIGMOD'00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data, 2000, 427-438.
Examples
data(mtcars)
data <- as.matrix(mtcars)
outl <- do_knno(data, 3, 2)
outl
data[outl,]
Degree of outlierness
Description
Classification of outliers according to their degree of outlierness. They are classified using the tolerance proportion. For instance, outliers from a 95
Usage
do_outl_degree(vect_tol = c(0.95, 0.9, 0.85), resid_vect, alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"))
Arguments
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85). |
resid_vect |
Vector of n residuals, where n was the number of rows of the data matrix. |
alpha |
Significance level. Default 0.05. |
outl_degree |
Type of outlier to identify the degree of outlierness. Default c("outl_strong", "outl_semi_strong", "outl_moderate"). |
Value
List with the type outliers.
Author(s)
Guillermo Vinue
See Also
Examples
do_outl_degree(0.95, 1:100, 0.05, "outl_strong")
Functional parallel archetypoid algorithm for large applications (FADALARA)
Description
The FADALARA algorithm is based on the CLARA clustering algorithm. This is the parallel version of the algorithm. It allows to detect anomalies (outliers). In the univariate case, there are two different methods to detect them: the adjusted boxplot (default and most reliable option) and tolerance intervals. In the multivariate case, only adjusted boxplots are used. If needed, tolerance intervals allow to define a degree of outlierness.
Usage
fadalara(data, N, m, numArchoid, numRep, huge, prob, type_alg = "fada",
compare = FALSE, PM, vect_tol = c(0.95, 0.9, 0.85), alpha = 0.05,
outl_degree = c("outl_strong", "outl_semi_strong", "outl_moderate"),
method = "adjbox", multiv, frame)
Arguments
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable. All variables are numeric. The data must have row names so that the algorithm can identify the archetypoids in every sample. |
N |
Number of samples. |
m |
Sample size of each sample. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
type_alg |
String. Options are 'fada' for the non-robust fadalara algorithm, whereas 'fada_rob' is for the robust fadalara algorithm. |
compare |
Boolean argument to compute the robust residual sum of squares
if |
PM |
Penalty matrix obtained with |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for
using adjusted boxplots for skewed distributions, and 'toler' for using
tolerance intervals.
The tolerance intervals are only computed in the univariate case, i.e.,
|
multiv |
Multivariate (TRUE) or univariate (FALSE) algorithm. |
frame |
Boolean value to indicate whether the frame is computed (Mair et al., 2017) or not. The frame is made up of a subset of extreme points, so the archetypoids are only computed on the frame. Low frame densities are obtained when only small portions of the data were extreme. However, high frame densities reduce this speed-up. |
Value
A list with the following elements:
cases Vector of archetypoids.
rss Optimal residual sum of squares.
outliers: Outliers.
alphas: Matrix with the alpha coefficients.
local_rel_imp Matrix with the local (casewise) relative importance (in percentage) of each variable for the outlier identification. Only for the multivariate case. It is relative to the outlier observation itself. The other observations are not considered for computing this importance. This procedure works because the functional variables are in the same scale, after standardizing. Otherwise, it couldn't be interpreted like that.
margi_rel_imp Matrix with the marginal relative importance of each variable (in percentage) for the outlier identification. Only for the multivariate case. In this case, the other points are considered, since the value of the outlier observation is compared with the remaining points.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Hubert, M. and Vandervieren, E., An adjusted boxplot for skewed distributions, 2008. Computational Statistics and Data Analysis 52(12), 5186-5201, https://doi.org/10.1016/j.csda.2007.11.008
Kaufman, L. and Rousseeuw, P.J., Clustering Large Data Sets, 1986. Pattern Recognition in Practice, 425-437.
Mair, S., Boubekki, A. and Brefeld, U., Frame-based Data Factorizations, 2017. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, 1-9.
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
# We have to give names to the dimensions to know the
# observations that were identified as archetypoids.
dimnames(Xs) <- list(paste("Obs", 1:dim(hgtm)[2], sep = ""),
1:nbasis,
c("boys", "girls"))
n <- dim(Xs)[1]
# Number of archetypoids:
k <- 3
numRep <- 20
huge <- 200
# Size of the random sample of observations:
m <- 15
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
data_alg <- Xs
# Parallel:
# Prepare parallelization (including the seed for reproducibility):
library(doParallel)
no_cores <- detectCores() - 1
no_cores
cl <- makeCluster(no_cores)
registerDoParallel(cl)
clusterSetRNGStream(cl, iseed = 2018)
res_fl <- fadalara(data = data_alg, N = N, m = m, numArchoid = k, numRep = numRep,
huge = huge, prob = prob, type_alg = "fada_rob", compare = FALSE,
PM = PM, method = "adjbox", multiv = TRUE, frame = FALSE) # frame = TRUE
stopCluster(cl)
res_fl_copy <- res_fl
res_fl <- res_fl[which.min(unlist(sapply(res_fl, function(x) x[2])))][[1]]
str(res_fl)
res_fl$cases
res_fl$rss
as.vector(res_fl$outliers)
## End(Not run)
Functional non-parallel archetypoid algorithm for large applications (FADALARA)
Description
The FADALARA algorithm is based on the CLARA clustering algorithm. This is the non-parallel version of the algorithm. It allows to detect anomalies (outliers). In the univariate case, there are two different methods to detect them: the adjusted boxplot (default and most reliable option) and tolerance intervals. In the multivariate case, only adjusted boxplots are used. If needed, tolerance intervals allow to define a degree of outlierness.
Usage
fadalara_no_paral(data, seed, N, m, numArchoid, numRep, huge, prob, type_alg = "fada",
compare = FALSE, verbose = TRUE, PM, vect_tol = c(0.95, 0.9, 0.85),
alpha = 0.05, outl_degree = c("outl_strong", "outl_semi_strong",
"outl_moderate"), method = "adjbox", multiv, frame)
Arguments
data |
Data matrix. Each row corresponds to an observation and each column corresponds to a variable (temporal point). All variables are numeric. The data must have row names so that the algorithm can identify the archetypoids in every sample. |
seed |
Integer value to set the seed. This ensures reproducibility. |
N |
Number of samples. |
m |
Sample size of each sample. |
numArchoid |
Number of archetypes/archetypoids. |
numRep |
For each |
huge |
Penalization added to solve the convex least squares problems. |
prob |
Probability with values in [0,1]. |
type_alg |
String. Options are 'fada' for the non-robust fadalara algorithm, whereas 'fada_rob' is for the robust fadalara algorithm. |
compare |
Boolean argument to compute the robust residual sum of squares
if |
verbose |
Display progress? Default TRUE. |
PM |
Penalty matrix obtained with |
vect_tol |
Vector the tolerance values. Default c(0.95, 0.9, 0.85).
Needed if |
alpha |
Significance level. Default 0.05. Needed if |
outl_degree |
Type of outlier to identify the degree of outlierness.
Default c("outl_strong", "outl_semi_strong", "outl_moderate").
Needed if |
method |
Method to compute the outliers. Options allowed are 'adjbox' for
using adjusted boxplots for skewed distributions, and 'toler' for using
tolerance intervals.
The tolerance intervals are only computed in the univariate case, i.e.,
|
multiv |
Multivariate (TRUE) or univariate (FALSE) algorithm. |
frame |
Boolean value to indicate whether the frame is computed (Mair et al., 2017) or not. The frame is made up of a subset of extreme points, so the archetypoids are only computed on the frame. Low frame densities are obtained when only small portions of the data were extreme. However, high frame densities reduce this speed-up. |
Value
A list with the following elements:
cases Vector of archetypoids.
rss Optimal residual sum of squares.
outliers: Vector of outliers.
alphas: Matrix with the alpha coefficients.
local_rel_imp Matrix with the local (casewise) relative importance (in percentage) of each variable for the outlier identification. Only for the multivariate case. It is relative to the outlier observation itself. The other observations are not considered for computing this importance. This procedure works because the functional variables are in the same scale, after standardizing. Otherwise, it couldn't be interpreted like that.
margi_rel_imp Matrix with the marginal relative importance of each variable (in percentage) for the outlier identification. Only for the multivariate case. In this case, the other points are considered, since the value of the outlier observation is compared with the remaining points.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Hubert, M. and Vandervieren, E., An adjusted boxplot for skewed distributions, 2008. Computational Statistics and Data Analysis 52(12), 5186-5201, https://doi.org/10.1016/j.csda.2007.11.008
Kaufman, L. and Rousseeuw, P.J., Clustering Large Data Sets, 1986. Pattern Recognition in Practice, 425-437.
Mair, S., Boubekki, A. and Brefeld, U., Frame-based Data Factorizations, 2017. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, 1-9.
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
# We have to give names to the dimensions to know the
# observations that were identified as archetypoids.
dimnames(Xs) <- list(paste("Obs", 1:dim(hgtm)[2], sep = ""),
1:nbasis,
c("boys", "girls"))
n <- dim(Xs)[1]
# Number of archetypoids:
k <- 3
numRep <- 20
huge <- 200
# Size of the random sample of observations:
m <- 15
# Number of samples:
N <- floor(1 + (n - m)/(m - k))
N
prob <- 0.75
data_alg <- Xs
seed <- 2018
res_fl <- fadalara_no_paral(data = data_alg, seed = seed, N = N, m = m,
numArchoid = k, numRep = numRep, huge = huge,
prob = prob, type_alg = "fada_rob", compare = FALSE,
verbose = TRUE, PM = PM, method = "adjbox", multiv = TRUE,
frame = FALSE) # frame = TRUE
str(res_fl)
res_fl$cases
res_fl$rss
as.vector(res_fl$outliers)
## End(Not run)
Compute archetypes frame
Description
Computing the frame with the approach by Mair et al. (2017).
Usage
frame_in_r(X)
Arguments
X |
Data frame. |
Value
Vector with the observations that belong to the frame.
Author(s)
Sebastian Mair, code kindly provided by him.
References
Mair, S., Boubekki, A. and Brefeld, U., Frame-based Data Factorizations, 2017. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia, 1-9.
Examples
## Not run:
X <- mtcars
q <- frame_in_r(X)
H <- X[q,]
q
## End(Not run)
Frobenius norm
Description
Computes the Frobenius norm.
Usage
frobenius_norm(m)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Guillermo Vinue, Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Vinue, G., Epifanio, I., and Alemany, S.,Archetypoids: a new approach to define representative archetypal data, 2015. Computational Statistics and Data Analysis 87, 102-115, https://doi.org/10.1016/j.csda.2015.01.018
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
Examples
mat <- matrix(1:4, nrow = 2)
frobenius_norm(mat)
Functional Frobenius norm
Description
Computes the functional Frobenius norm.
Usage
frobenius_norm_funct(m, PM)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
PM |
Penalty matrix obtained with |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Examples
library(fda)
mat <- matrix(1:9, nrow = 3)
fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3)
PM <- eval.penalty(fbasis)
frobenius_norm_funct(mat, PM)
Functional multivariate Frobenius norm
Description
Computes the functional multivariate Frobenius norm.
Usage
frobenius_norm_funct_multiv(m, PM)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
PM |
Penalty matrix obtained with |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Irene Epifanio
References
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Examples
mat <- matrix(1:400, ncol = 20)
PM <- matrix(1:100, ncol = 10)
frobenius_norm_funct_multiv(mat, PM)
Functional multivariate robust Frobenius norm
Description
Computes the functional multivariate robust Frobenius norm.
Usage
frobenius_norm_funct_multiv_robust(m, PM, prob, nbasis, nvars)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
nbasis |
Number of basis. |
nvars |
Number of variables. |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
mat <- matrix(1:400, ncol = 20)
PM <- matrix(1:100, ncol = 10)
frobenius_norm_funct_multiv_robust(mat, PM, 0.8, 10, 2)
Functional robust Frobenius norm
Description
Computes the functional robust Frobenius norm.
Usage
frobenius_norm_funct_robust(m, PM, prob)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
library(fda)
mat <- matrix(1:9, nrow = 3)
fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3)
PM <- eval.penalty(fbasis)
frobenius_norm_funct_robust(mat, PM, 0.8)
Robust Frobenius norm
Description
Computes the robust Frobenius norm.
Usage
frobenius_norm_robust(m, prob)
Arguments
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
prob |
Probability with values in [0,1]. |
Details
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Value
Real number.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
mat <- matrix(1:4, nrow = 2)
frobenius_norm_robust(mat, 0.8)
Interior product between matrices
Description
Helper function to compute the Frobenius norm.
Usage
int_prod_mat(m)
Arguments
m |
Data matrix. |
Value
Data matrix.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
mat <- matrix(1:4, nrow = 2)
int_prod_mat(mat)
Interior product between matrices for FDA
Description
Helper function to compute the Frobenius norm in the functional data analysis (FDA) scenario.
Usage
int_prod_mat_funct(m, PM)
Arguments
m |
Data matrix. |
PM |
Penalty matrix obtained with |
Value
Data matrix.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
library(fda)
mat <- matrix(1:9, nrow = 3)
fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3)
PM <- eval.penalty(fbasis)
int_prod_mat_funct(mat, PM)
Squared interior product between matrices
Description
Helper function to compute the robust Frobenius norm.
Usage
int_prod_mat_sq(m)
Arguments
m |
Data matrix. |
Value
Data matrix.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
mat <- matrix(1:4, nrow = 2)
int_prod_mat_sq(mat)
Squared interior product between matrices for FDA
Description
Helper function to compute the robust Frobenius norm in the functional data analysis (FDA) scenario.
Usage
int_prod_mat_sq_funct(m, PM)
Arguments
m |
Data matrix. |
PM |
Penalty matrix obtained with |
Value
Data matrix.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
library(fda)
mat <- matrix(1:9, nrow = 3)
fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3)
PM <- eval.penalty(fbasis)
int_prod_mat_sq_funct(mat, PM)
Tolerance outliers
Description
Outliers according to a tolerance interval. This function is used by
the archetypoid algorithms to identify the outliers. See the function
nptol.int in package tolerance.
Usage
outl_toler(p_tol = 0.95, resid_vect, alpha = 0.05)
Arguments
p_tol |
The proportion of observations to be covered by this tolerance interval. |
resid_vect |
Vector of n residuals, where n was the number of rows of the data matrix. |
alpha |
Significance level. |
Value
Vector with the outliers.
Author(s)
Guillermo Vinue
References
Young, D., tolerance: An R package for estimating tolerance intervals, 2010. Journal of Statistical Software, 36(5), 1-39, https://doi.org/10.18637/jss.v036.i05
See Also
adalara, fadalara, do_outl_degree
Examples
outl_toler(0.95, 1:100, 0.05)
Archetype algorithm to raw data with the functional Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the functional archetype algorithm with the Frobenius norm.
Usage
stepArchetypesRawData_funct(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE, PM)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
PM |
Penalty matrix obtained with |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Cutler, A. and Breiman, L., Archetypal Analysis. Technometrics, 1994, 36(4), 338-347, https://doi.org/10.2307/1269949
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
lass <- stepArchetypesRawData_funct(data = data_archs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM)
str(lass)
length(lass[[1]])
class(lass[[1]])
class(lass[[1]][[5]])
## End(Not run)
Archetype algorithm to raw data with the functional multivariate Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the functional archetype algorithm with the multivariate Frobenius norm.
Usage
stepArchetypesRawData_funct_multiv(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE, PM)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
PM |
Penalty matrix obtained with |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Cutler, A. and Breiman, L., Archetypal Analysis. Technometrics, 1994, 36(4), 338-347, https://doi.org/10.2307/1269949
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
lass <- stepArchetypesRawData_funct_multiv(data = Xs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM)
str(lass)
length(lass[[1]])
class(lass[[1]])
class(lass[[1]][[5]])
## End(Not run)
Archetype algorithm to raw data with the functional multivariate robust Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the functional archetype algorithm with the multivariate Frobenius norm.
Usage
stepArchetypesRawData_funct_multiv_robust(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE, PM, prob, nbasis, nvars)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
nbasis |
Number of basis. |
nvars |
Number of variables. |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Cutler, A. and Breiman, L., Archetypal Analysis. Technometrics, 1994, 36(4), 338-347, https://doi.org/10.2307/1269949
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- growth$hgtm
hgtf <- growth$hgtf[,1:39]
# Create array:
nvars <- 2
data.array <- array(0, dim = c(dim(hgtm), nvars))
data.array[,,1] <- as.matrix(hgtm)
data.array[,,2] <- as.matrix(hgtf)
rownames(data.array) <- 1:nrow(hgtm)
colnames(data.array) <- colnames(hgtm)
str(data.array)
# Create basis:
nbasis <- 10
basis_fd <- create.bspline.basis(c(1,nrow(hgtm)), nbasis)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:nrow(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = data.array, basisobj = basis_fd)
X <- array(0, dim = c(dim(t(temp_fd$coefs[,,1])), nvars))
X[,,1] <- t(temp_fd$coef[,,1])
X[,,2] <- t(temp_fd$coef[,,2])
# Standardize the variables:
Xs <- X
Xs[,,1] <- scale(X[,,1])
Xs[,,2] <- scale(X[,,2])
lass <- stepArchetypesRawData_funct_multiv_robust(data = Xs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM, prob = 0.8,
nbasis, nvars)
str(lass)
length(lass[[1]])
class(lass[[1]])
class(lass[[1]][[5]])
## End(Not run)
Archetype algorithm to raw data with the functional robust Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the functional archetype algorithm with the functional robust Frobenius norm.
Usage
stepArchetypesRawData_funct_robust(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE, PM, prob)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
PM |
Penalty matrix obtained with |
prob |
Probability with values in [0,1]. |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Cutler, A. and Breiman, L., Archetypal Analysis. Technometrics, 1994, 36(4), 338-347, https://doi.org/10.2307/1269949
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Examples
## Not run:
library(fda)
?growth
str(growth)
hgtm <- t(growth$hgtm)
# Create basis:
basis_fd <- create.bspline.basis(c(1,ncol(hgtm)), 10)
PM <- eval.penalty(basis_fd)
# Make fd object:
temp_points <- 1:ncol(hgtm)
temp_fd <- Data2fd(argvals = temp_points, y = growth$hgtm, basisobj = basis_fd)
data_archs <- t(temp_fd$coefs)
lass <- stepArchetypesRawData_funct_robust(data = data_archs, numArch = 3,
numRep = 5, verbose = FALSE,
saveHistory = FALSE, PM, prob = 0.8)
str(lass)
length(lass[[1]])
class(lass[[1]])
class(lass[[1]][[5]])
## End(Not run)
Archetype algorithm to raw data with the Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the archetype algorithm with the Frobenius norm.
Usage
stepArchetypesRawData_norm_frob(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Eugster, M.J.A. and Leisch, F., From Spider-Man to Hero - Archetypal Analysis in R, 2009. Journal of Statistical Software 30(8), 1-23, https://doi.org/10.18637/jss.v030.i08
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
Vinue, G., Epifanio, I., and Alemany, S., Archetypoids: a new approach to define representative archetypal data, 2015. Computational Statistics and Data Analysis 87, 102-115, https://doi.org/10.1016/j.csda.2015.01.018
Vinue, G., Anthropometry: An R Package for Analysis of Anthropometric Data, 2017. Journal of Statistical Software 77(6), 1-39, https://doi.org/10.18637/jss.v077.i06
See Also
stepArchetypesRawData,
stepArchetypes
Examples
data(mtcars)
data <- as.matrix(mtcars)
numArch <- 5
numRep <- 2
lass <- stepArchetypesRawData_norm_frob(data = data, numArch = 1:numArch,
numRep = numRep, verbose = FALSE)
str(lass)
length(lass[[1]])
class(lass[[1]])
Archetype algorithm to raw data with the robust Frobenius norm
Description
This is a slight modification of stepArchetypesRawData
to use the archetype algorithm with the robust Frobenius norm.
Usage
stepArchetypesRawData_robust(data, numArch, numRep = 3,
verbose = TRUE, saveHistory = FALSE, prob)
Arguments
data |
Data to obtain archetypes. |
numArch |
Number of archetypes to compute, from 1 to |
numRep |
For each |
verbose |
If TRUE, the progress during execution is shown. |
saveHistory |
Save execution steps. |
prob |
Probability with values in [0,1]. |
Value
A list with the archetypes.
Author(s)
Irene Epifanio
References
Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036
See Also
stepArchetypesRawData_norm_frob
Examples
data(mtcars)
data <- as.matrix(mtcars)
numArch <- 5
numRep <- 2
lass <- stepArchetypesRawData_robust(data = data, numArch = 1:numArch,
numRep = numRep, verbose = FALSE,
saveHistory = FALSE, prob = 0.8)
str(lass)
length(lass[[1]])
class(lass[[1]])