| Title: | Maximum Diversity Weighting |
|---|---|
| Description: | Dimension-reduction methods aim at defining a score that maximizes signal diversity. Three approaches, tree weight, maximum entropy weights, and maximum variance weights are provided. These methods are described in He and Fong (2019) <DOI:10.1002/sim.8212>. |
| Authors: | Zonglin He [aut], Youyi Fong [cre] |
| Maintainer: | Youyi Fong <[email protected]> |
| License: | GPL-2 |
| Version: | 2024.8-1 |
| Built: | 2025-01-20 05:26:16 UTC |
| Source: | https://github.com/cran/mdw |
asym.v.e produces estimated asymptotic covariance matrix of the first p-1 maximum entropy weights (because the p weights sum to 1).
asym.v.e(X, w, h)asym.v.e(X, w, h)
X |
n by p maxtrix containing observations of p biomarkers of n subjects. |
w |
maximum entropy weights for dateset X with bandwidth h used |
h |
bandwidth for kernel density estimation. |
library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) h = 1 w <- entropy.weight(X,h) asym.v.e(X,w,h)library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) h = 1 w <- entropy.weight(X,h) asym.v.e(X,w,h)
asym.v.v produces estimated asymptotic covariance matrix of the first p-1 maximum variance weights (because the p weights sum to 1).
asym.v.v(X, w)asym.v.v(X, w)
X |
n by p maxtrix containing observations of p biomarkers of n subjects. |
w |
maximum variance weights for dateset X |
library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) w <- var.weight(X) asym.v.v(X,w)library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) w <- var.weight(X) asym.v.v(X,w)
entropy.weight produces a set of weights that maximizes the total weighted entropy of the distribution of different biomarkers within each subject, values of biomarkers can be either continuous or categorical.
entropy.weight(X, h)entropy.weight(X, h)
X |
n by p maxtrix containing observations of p biomarkers of n subjects. |
h |
bandwidth for kernel density estimation. if data is categorical, set to 'na'. |
library(MASS) # a three biomarkers dataset generated from independent normal(0,1) set.seed(1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) entropy.weight(X, h=1) ### # a three categorical biomarkers dataset set.seed(1) tmp=mvrnorm(n=10,mu=c(0,0,0),Sigma = diag(3)) dat=t(apply(tmp, 1, function(x) cut(x,c(-Inf,-0.5,0.5,Inf),labels=1:3))) entropy.weight(dat,h='na')library(MASS) # a three biomarkers dataset generated from independent normal(0,1) set.seed(1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) entropy.weight(X, h=1) ### # a three categorical biomarkers dataset set.seed(1) tmp=mvrnorm(n=10,mu=c(0,0,0),Sigma = diag(3)) dat=t(apply(tmp, 1, function(x) cut(x,c(-Inf,-0.5,0.5,Inf),labels=1:3))) entropy.weight(dat,h='na')
get.bw applies a specified bandwidth selection method to the dataset subject-wisely and return the median of the n selected bandwidths as the choice of bandwidth for entropy.weight.
get.bw(x, bw = c("nrd", "ucv", "bcv", "SJ"), nb)get.bw(x, bw = c("nrd", "ucv", "bcv", "SJ"), nb)
x |
n by p maxtrix containing observations of p biomarkers of n subjects. |
bw |
bandwidth selectors of nrd, ucv, bcv, and SJ corresponding to R functions bw.nrd, bw.ucv, bw.bcv, and bw.SJ. |
nb |
number of bins to use, 'na' if bw='nrd' |
library(MASS) # a ten biomarkers dataset generated from independent normal(0,1) x = mvrnorm(n = 100, mu=rep(0,10), Sigma=diag(10), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) get.bw(x,bw='ucv',nb=100) get.bw(x,bw='nrd',nb='na')library(MASS) # a ten biomarkers dataset generated from independent normal(0,1) x = mvrnorm(n = 100, mu=rep(0,10), Sigma=diag(10), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) get.bw(x,bw='ucv',nb=100) get.bw(x,bw='nrd',nb='na')
pca.weight produce the coefficients of the first principal compoment
pca.weight(emp.cor)pca.weight(emp.cor)
emp.cor |
empirical correlation matrix of the dataset |
library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) emp.cor <- cor(X) pca.weight(emp.cor)library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) emp.cor <- cor(X) pca.weight(emp.cor)
tree.weight Produce a set of weights for different end points based on a correlation matrix using the GSC tree method
tree.weight (cor.mat, method="GSC", clustering.method="average", plot=TRUE, orientation=c("vertical","horizontal"), ...)tree.weight (cor.mat, method="GSC", clustering.method="average", plot=TRUE, orientation=c("vertical","horizontal"), ...)
cor.mat |
a matrix, correlation matrix |
method |
a string. GSC, implementation of Gerstein et al., is the only implemented currently |
clustering.method |
a string, how the bottom-up hierarchical clustering tree is built, is passed to hclust as the method parameter |
plot |
a Boolean, whether to plot the tree |
orientation |
vertical or horizontal |
... |
additional args |
A vector of weights that sum to 1.
Youyi Fong [email protected]
Gerstein, M., Sonnhammer, E., and Chothia, C. (1994), Volume changes in protein evolution. J Mol Biol, 236, 1067-78.
cor.mat=diag(rep(1,3)) cor.mat[1,2]<-cor.mat[2,1]<-0.9 cor.mat[1,3]<-cor.mat[3,1]<-0.1 cor.mat[2,3]<-cor.mat[3,2]<-0.1 tree.weight(cor.mat)cor.mat=diag(rep(1,3)) cor.mat[1,2]<-cor.mat[2,1]<-0.9 cor.mat[1,3]<-cor.mat[3,1]<-0.1 cor.mat[2,3]<-cor.mat[3,2]<-0.1 tree.weight(cor.mat)
var.weight produces a set of weights that maximizes the total weighted variance of the distribution of different biomarkers within each subject.
var.weight(X, method = c("optim", "mosek"))var.weight(X, method = c("optim", "mosek"))
X |
n by p maxtrix containing observations of p biomarkers of n subjects. |
method |
optim (default) using R constrOptim function from stats package for optimization, mosek using mosek function from Rmosek package for optimization |
library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) # compute maximum variance weights using constrOptim for optimization var.weight(X) ## Not run: # need mosek installed # compute maximum variance weights using mosek for optimization library(Rmosek) var.weight(X,'mosek') ## End(Not run)library(MASS) # a three biomarkers dataset generated from independent normal(0,1) X = mvrnorm(n = 100, mu=rep(0,3), Sigma=diag(3), tol = 1e-6, empirical = FALSE, EISPACK = FALSE) # compute maximum variance weights using constrOptim for optimization var.weight(X) ## Not run: # need mosek installed # compute maximum variance weights using mosek for optimization library(Rmosek) var.weight(X,'mosek') ## End(Not run)