View source: R/depth.projection.r
depth.projection  R Documentation 
Calculates the projection depth of points w.r.t. a multivariate data set.
depth.projection(x, data, method = "random", num.directions = 1000, seed = 0)
x 
Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a dvariate point. Should have the same dimension as 
data 
Matrix of data where each row contains a dvariate point, w.r.t. which the depth is to be calculated. 
method 
to be used in calculations.

num.directions 
Number of random directions to be generated for 
seed 
the random seed. The default value 
Calculates projection depth. Projection depth, similar to Mahalanobis depth, is based on a measure of outlyingness, used by Stahel (1981) and Donoho (1982), and has been first formulated by Liu (1992). The worst case outlyingness is obtained by maximizing an outlyingness measure over all univariate projections. In practice most often median, and median absolute deviation from the median (MAD), are used as they are robust measures.
Numerical vector of depths, one for each row in x
; or one depth value if x
is a numerical vector.
Rcodes for the "linearize" method were written by Subhajit Dutta.
Donoho, D.L. (1982). Breakdown properties of multivariate location estimators. Ph.D. qualifying paper. Department of Statistics, Harvard University.
Liu, R.Y. (1992). Data depth and multivariate rank tests. In: Dodge, Y. (ed.), L1Statistics and Related Methods, NorthHolland (Amsterdam), 279–294.
Liu, X. and Zuo, Y. (2014). Computing projection depth and its associated estimators. Statistics and Computing 24 51–63.
Stahel, W.A. (1981). Robust estimation: infinitesimal optimality and covariance matrix estimators. Ph.D. thesis (in German). Eidgenossische Technische Hochschule Zurich.
Zuo, Y.J. and Lai, S.Y. (2011). Exact computation of bivariate projection depth and the StahelDonoho estimator. Computational Statistics and Data Analysis 55 1173–1179.
depth.halfspace
for calculation of the Tukey depth.
depth.Mahalanobis
for calculation of Mahalanobis depth.
depth.simplicial
for calculation of simplicial depth.
depth.simplicialVolume
for calculation of simplicial volume depth.
depth.spatial
for calculation of spatial depth.
depth.zonoid
for calculation of zonoid depth.
depth.potential
for calculation of data potential.
# 5dimensional normal distribution data < mvrnorm(100, rep(0, 5), matrix(c(1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1), nrow = 5)) x < mvrnorm(10, rep(1, 5), matrix(c(1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1), nrow = 5)) depths < depth.projection(x, data, method = "random", num.directions = 1000) cat("Depths random: ", depths, "\n") depths < depth.projection(x, data, method = "linearize") cat("Depths linearize: ", depths, "\n")
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