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)))