| localdepth.similarity {localdepth} | R Documentation |
The function evaluates depth and local depth similarity for a set of points with respect to a dataset.
localdepth.similarity(x, y = NULL, tau, use = c("volume", "diameter"),
method = c("simplicial", "ellipsoid", "mahalanobis"),
type = c("exact", "approx"), nsamp = "all", nmax = 1,
tol = 10^(-9), dimension=NULL, location = NULL, covariance = NULL,
weight = NULL)
x |
numeric; vector, dataframe or matrix. If x is a circular vector, a circular version is used. Avoid ties by wiggling the data. The function only issues a warning for ties. |
y |
numeric; vector, dataframe or matrix with the same number of columns as x, or NULL. If NULL, x is used |
tau |
numeric; threshold value for the evaluation of the local depth. Use function quantile.localdepth to evaluate tau using a quantile of the size of the objects |
use |
character; the statistic used to measure the size of the objects. Currently, for method equal to "simplicial" or "ellipsoid" allowed statistics are "volume" and "diameter". For method equal to "mahalanobis" this parameter is not used and the only available statistic is pairwise Mahalanobis' distance |
method |
character; the type of (local) depth similarity to be evaluated |
type |
character; how to evaluate membership. Only active for method="simplicial". See details. |
nsamp |
character or numeric; the number of objects that are considered. If "all", the size of all choose(NROW(x), NCOL(x)+1) objects is evaluated. Otherwise, a simple random sample with replacement of size nsamp is performed from the set of all possible objects. |
nmax |
numeric; maximum fraction (in the range (0,1]) of objects to be considered when nsamp is not equal to all. If nmax=1 the number of searched objects can reach the number of possible objects (choose(NROW(x), NCOL(x)+1) for simplicial and ellipsoid depth) |
tol |
numeric; tolerance parameter to be fixed depending on the machine precision. Used to decide membership of points located near to the boundary of the objects |
dimension |
numeric; only used with method="ellipsoid". It is the squared length of the ellipsoid semimajor axis. If dimension is NULL, it is set to NCOL(x) |
location |
NULL or a numeric vector; the NCOL(x) means vector used in method equal to "mahalanobis". If NULL, apply(x, 2, mean) is used |
covariance |
NULL or a numeric matrix; the NCOL(x)*NCOL(x) covariance matrix used in method equal to "mahalanobis". If NULL, cov(x) is used |
weight |
experimental parameter used to weight entries in the similarity matrix. Not implemented in each method, dimension. |
With method="simplicial" and type="exact", membership of the points in simplices is evaluated; when type="approx", an approximate membership function is used. See references below.
The function returns an object of class localdepth.similarity with the following components:
localdepth |
matrix of the local depth similarities |
depth |
matrix of the depth similarities |
max.localdepth |
max(localdepth) |
max.depth |
max(depth) |
num |
vector with two components. num[1] gives the number of objects used for the evaluation of the depth similarity; num[2] is the number of objects used for the evaluation of the local depth similarity |
call |
match.call() result. Note that this is called from the internal function |
tau |
value of the corresponding input parameter |
use |
value of the corresponding input parameter |
tol |
value of the corresponding input parameter |
x |
value of the corresponding input parameter |
y |
value of the corresponding input parameter |
type |
value of the corresponding input parameter |
nsamp |
value of the corresponding input parameter |
method |
value of the corresponding input parameter |
The function is not yet implemented for Ellipsoid (local) depth.
Claudio Agostinelli and Mario Romanazzi
C. Agostinelli and M. Romanazzi (2007). Local depth of univariate distributions. Working paper n. 1/2007, Dipartimento di Statistica, Universita' Ca' Foscari, Venezia.
C. Agostinelli and M. Romanazzi (2008). Local depth of multidimensional data. Working paper n. 3/2008, Dipartimento di Statistica, Universita' Ca' Foscari, Venezia.
R.Y. Liu, J.M. Parelius and K. Singh (1999) Multivariate analysis by data depth: descriptive statistics, graphics and inference. The Annals of Statistics, 27, 783-858.
data(cork) tau <- quantile.localdepth(cork[,c(1,3)], probs=0.1, method='simplicial') sim <- localdepth.similarity(cork[,c(1,3)], tau=tau, method='simplicial') plot(hclust(d=as.dist(1-sim$localdepth/sim$max.localdepth))) plot(hclust(d=as.dist(1-sim$depth/sim$max.depth)))