pdDepth calculates the data depth of a HPD matrix with respect
to a given data cloud (i.e., a sample or collection) of HPD matrices, or the integrated
data depth of a sequence (curve) of HPD matrices with respect to a given data cloud of
sequences (curves) of HPD matrices as detailed in \insertCiteCOvS17pdSpecEst.
either a (d,d)-dimensional HPD matrix, or a (d, d, n)-dimensional array corresponding to a sequence
or curve of HPD matrices. Defaults to
depending on the input
the data depth measure, one of
the metric that the space of HPD matrices is equipped with. The default choice is
Available pointwise or integrated intrinsic data depth functions for samples of HPD matrices are: (i)
geodesic distance depth, (ii) intrinsic zonoid depth and (iii) intrinsic spatial depth.
The various data depth measures and their theoretical properties are described in
y is a (d,d)-dimensional HPD matrix,
X should be a (d,d,S)-dimensional array
corresponding to a length
S sequence of (d,d)-dimensional HPD matrices and the pointwise
data depth values are computed. If
y is a sequence of (d,d)-dimensional HPD matrices of length
(i.e., (d,d,n)-dimensional array),
X should be a (d,d,n,S)-dimensional array of replicated sequences of HPD matrices
and the integrated data depth values according to \insertCiteCOvS17pdSpecEst are computed. If
is.null(y), the data depth
of each individual object (i.e., a HPD matrix or a sequence of HPD matrices) in
X is computed with
respect to the data cloud
The function computes the intrinsic data depth values based on the metric space of HPD matrices equipped with one of the following metrics: (i) Riemannian metric (default) as detailed in e.g., \insertCiteB09pdSpecEst[Chapter 6] or \insertCitePFA05pdSpecEst, (ii) log-Euclidean metric, the Euclidean inner product between matrix logarithms, (iii) Cholesky metric, the Euclidean inner product between Cholesky decompositions, (iv) Euclidean metric and (v) root-Euclidean metric. The default choice (Riemannian) has several properties not shared by the other metrics, see \insertCiteCOvS17pdSpecEst for more details.
pdDepth returns the numeric depth value of
pdDepth returns a numeric vector of length
S corresponding to
the vector of depth values for each individual object in
X with respect to
The function does not check for positive definiteness of the input matrices, and may fail if matrices are close to being singular.
The data depth computations under the Riemannian metric are more involved than under the other metrics, and may therefore result in (significantly) higher computation times.
1 2 3 4 5 6 7 8 9
## Pointwise depth X1 <- replicate(50, Expm(diag(2), H.coeff(rnorm(4), inverse = TRUE))) pdDepth(y = diag(2), X = X1) ## depth of one point pdDepth(X = X1) ## depth of each point in the data cloud ## Integrated depth X2 <- replicate(50, replicate(5, Expm(diag(2), H.coeff(rnorm(4), inverse = TRUE)))) pdDepth(y = replicate(5, diag(2)), X2, method = "zonoid", metric = "logEuclidean") pdDepth(X = X2, method = "zonoid", metric = "logEuclidean")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.