Computation of depth measures for functional data
Several depth measures can be computed for functional data for descriptive or classification purposes.
depth.mode( fdataobj, fdataori = fdataobj, trim = 0.25, metric = metric.lp, h = NULL, scale = FALSE, draw = FALSE, ... ) depth.RP( fdataobj, fdataori = fdataobj, trim = 0.25, nproj = 50, proj = "vexponential", dfunc = "TD1", par.dfunc = list(), scale = FALSE, draw = FALSE, ... ) depth.RPD( fdataobj, fdataori = fdataobj, nproj = 20, proj = 1, deriv = c(0, 1), trim = 0.25, dfunc2 = mdepth.LD, method = "fmm", draw = FALSE, ... ) depth.RT( fdataobj, fdataori = fdataobj, trim = 0.25, nproj = 10, proj = 1, xeps = 1e-07, draw = FALSE, ... ) depth.KFSD( fdataobj, fdataori = fdataobj, trim = 0.25, h = NULL, scale = FALSE, draw = FALSE ) depth.FSD( fdataobj, fdataori = fdataobj, trim = 0.25, scale = FALSE, draw = FALSE ) depth.FM( fdataobj, fdataori = fdataobj, trim = 0.25, scale = FALSE, dfunc = "FM1", par.dfunc = list(scale = TRUE), draw = FALSE )
fdataobj |
The set of new curves to evaluate the depth.
|
fdataori |
The set of reference curves respect to which the depth is
computed. |
trim |
The alpha of the trimming. |
metric |
Metric function, by default |
h |
Bandwidth parameter.
|
scale |
=TRUE, the depth is scaled respect to depths in
|
draw |
=TRUE, draw the curves, the sample median and trimmed mean. |
... |
Further arguments passed to or from other methods. For
|
nproj |
The number of projections. Ignored if a |
proj |
if a |
dfunc |
type of univariate depth function used inside depth function:
"FM1" refers to the original Fraiman and Muniz univariate depth (default),
"TD1" Tukey (Halfspace),"Liu1" for simplical depth, "LD1" for Likelihood
depth and "MhD1" for Mahalanobis 1D depth. Also, any user function
fulfilling the following pattern |
par.dfunc |
List of parameters for dfunc. |
deriv |
Number of derivatives described in integer vector |
dfunc2 |
Multivariate depth function (second step depth function) in
RPD depth, by default |
method |
Type of derivative method. See |
xeps |
Accuracy. The left limit of the empirical distribution function. |
Type of depth functions: Fraiman and Muniz (FM) depth, modal depth, random Tukey (RT), random projection (RP) depth and double random projection depth (RPD).
depth.FM computes the integration of an univariate depth
along the axis x (see Fraiman and Muniz 2001). It is also known as
Integrated Depth.
depth.mode implements the modal depth (see Cuevas et al
2007).
depth.RT implements the Random Tukey depth (see
Cuesta–Albertos and Nieto–Reyes 2008).
depth.RP computes the Random Projection depth (see
Cuevas et al. 2007).
depth.RPD implements a depth measure based on random
projections possibly using several derivatives (see Cuevas et al. 2007).
depth.FSD computes the Functional Spatial Depth (see
Sguera et al. 2014).
depth.KFSD implements the Kernelized Functional Spatial
Depth (see Sguera et al. 2014).
The depth.mode function calculates the depth of a datum
accounting the number of curves in its neighbourhood. By default, the
distance is calculated using metric.lp function although any
other distance could be employed through argument metric (with the
general pattern USER.DIST(fdataobj,fdataori)).
The depth.RP function summarizes the random projections
through averages whereas the depth.RT function uses the
minimum of all projections.
The depth.RPD function involves the original
trajectories and the derivatives of each curve in two steps. It builds
random projections for the function and their derivatives (indicated in the
parameter deriv) and then applies a depth function (by default
depth.mode) to this set of random projections (by default the
Tukey one).
The depth.FSD and depth.KFSD are the
implementations of the default versions of the functional spatial depths
proposed in Sguera et al 2014. At this moment, it is not possible to change
the kernel in the second one.#'
Return a list with:
median Deepest curve.
lmed Index deepest element median.
mtrim fdata class object with the average from the (1-trim)% deepest curves.
ltrim Indexes of curves that conform the trimmed mean mtrim.
dep Depth of each curve of fdataobj w.r.t. fdataori.
dep.ori Depth of each curve of fdataori w.r.t. fdataori.
proj The projection value of each point on the curves.
dist Distance matrix between curves or functional data.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
Cuevas, A., Febrero-Bande, M., Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics 22, 3, 481-496.
Fraiman R, Muniz G. (2001). Trimmed means for functional data. Test 10: 419-440.
Cuesta–Albertos, JA, Nieto–Reyes, A. (2008) The Random Tukey Depth. Computational Statistics and Data Analysis Vol. 52, Issue 11, 4979-4988.
Febrero-Bande, M, Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/
Sguera C, Galeano P, Lillo R (2014). Spatial depth based classification for functional data. TEST 23(4):725–750.
See Also as Descriptive.
## Not run:
#Ex: CanadianWeather data
tt=1:365
fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]),tt)
# Fraiman-Muniz Depth
out.FM=depth.FM(fdataobj,trim=0.1,draw=TRUE)
#Modal Depth
out.mode=depth.mode(fdataobj,trim=0.1,draw=TRUE)
out.RP=depth.RP(fdataobj,trim=0.1,draw=TRUE)
out.RT=depth.RT(fdataobj,trim=0.1,draw=TRUE)
out.FSD=depth.FSD(fdataobj,trim=0.1,draw=TRUE)
out.KFSD=depth.KFSD(fdataobj,trim=0.1,draw=TRUE)
## Double Random Projections
out.RPD=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=mdepth.LD,
trim=0.1,draw=TRUE)
out<-c(out.FM$mtrim,out.mode$mtrim,out.RP$mtrim,out.RPD$mtrim)
plot(fdataobj,col="grey")
lines(out)
cdep<-cbind(out.FM$dep,out.mode$dep,out.RP$dep,out.RT$dep,out.FSD$dep,out.KFSD$dep)
colnames(cdep)<-c("FM","mode","RP","RT","FSD","KFSD")
pairs(cdep)
round(cor(cdep),2)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.