| Title: | Graph-Based k-Sample Comparisons and Relevance Analysis in High Dimensions |
| Version: | 1.0 |
| Imports: | mvtnorm,MASS,philentropy |
| Description: | We propose two distribution-free test statistics based on between-sample edge counts and measure the degree of relevance by standardized counts. Users can set edge costs in the graph to compare the parameters of the distributions. Methods for comparing distributions are as described in: Xiaoping Shi (2021) <doi:10.48550/arXiv.2107.00728>. |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.0 |
| Depends: | R (≥ 2.10) |
| License: | MIT + file LICENSE |
| NeedsCompilation: | no |
| Packaged: | 2023-02-22 03:27:49 UTC; xshi |
| Author: | Xiaoping Shi 
[aut, cre] |
| Maintainer: | Xiaoping Shi <xiaoping.shi@ubc.ca> |
| Repository: | CRAN |
| Date/Publication: | 2023-02-22 15:10:12 UTC |
Basic description
Description
Applies the path.kruskal function based on the nodes and edge.cost (sorts the weights from minimum to maximum). Given the starting node, ending node, and the distance matrix, this function returns the list of nodes of each edge from the shortest Hamiltonian path. We have the Hamiltonian path from path.kruskal
Usage
Hpath(n1,n2,mat)
Arguments
n1 |
starting node |
n2 |
ending node |
mat |
distance matrix (distance type is determined by the reader) |
Value
list of nodes of each edge from the shortest Hamiltonian path
See Also
path.kruskal
Examples
G=list()
set.seed(1)
n1=20;n2=40
N=n1+n2;
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));
d=10
mu1=rep(0,d)
mu2=mu1+0.1
true.cov1=0.4^(abs(outer(1:d,1:d,"-")))
true.cov2=0.4^(abs(outer(1:d,1:d,"-")))
sam1=MASS::mvrnorm(n=n1,mu=mu1,Sigma=true.cov1)
sam2=MASS::mvrnorm(n=n2,mu=mu2,Sigma=true.cov2)
Data=rbind(sam1,sam2)
Dist=philentropy::distance(Data, method = "euclidean")
Dist[lower.tri(Dist)] <- NA
Dist[diag(Dist)] <- NA
Hpath(1,N,Dist)
Basic description
Description
Given the groups and the observed statistic, this function returns the pvalue.
Usage
Mpermut(G,W,obs)
Arguments
G |
a list of all groups |
W |
the weight matrix |
obs |
the observed statistic |
Value
the pvalue
Examples
G=list()
set.seed(1)
n1=20;n2=40
N=n1+n2;
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));
d=10
mu1=rep(0,d)
mu2=mu1+0.1
true.cov1=0.4^(abs(outer(1:d,1:d,"-")))
true.cov2=0.4^(abs(outer(1:d,1:d,"-")))
sam1=MASS::mvrnorm(n=n1,mu=mu1,Sigma=true.cov1)
sam2=MASS::mvrnorm(n=n2,mu=mu2,Sigma=true.cov2)
Data=rbind(sam1,sam2)
Dist=philentropy::distance(Data, method = "euclidean")
Dist[lower.tri(Dist)] <- NA
Dist[diag(Dist)] <- NA
counts=compbypath(G,Hpath(1,N,Dist))
W=Weight(G)
#W[i,j]=0 #if we donot consider this relevance between sample i and sample j
C=counts$EC
Z=(C-W$mean)*W$weight
obs=min(Z[!is.na(Z)])
Mpermut(G,W$weight,obs)
Basic description
Description
Given the sampless, this function returns the mean and weight matrix.
Usage
Weight(G)
Arguments
G |
a list of all groups |
Value
the mean and weight matrix
Examples
G=list()
set.seed(1)
n1=20;n2=40
N=n1+n2;
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));
Weight(G)
Basic description
Description
Given the groups, the weight matrix and the observed statistic, this function returns the pvalue.
Usage
Wpermut(G,W,obs)
Arguments
G |
a list of all groups |
W |
the weight matrix |
obs |
the observed statistic |
Value
the pvalue
Examples
G=list()
set.seed(1)
n1=20;n2=40
N=n1+n2;
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));
d=10
mu1=rep(0,d)
mu2=mu1+0.1
true.cov1=0.4^(abs(outer(1:d,1:d,"-")))
true.cov2=0.4^(abs(outer(1:d,1:d,"-")))
sam1=MASS::mvrnorm(n=n1,mu=mu1,Sigma=true.cov1)
sam2=MASS::mvrnorm(n=n2,mu=mu2,Sigma=true.cov2)
Data=rbind(sam1,sam2)
Dist=philentropy::distance(Data, method = "euclidean")
Dist[lower.tri(Dist)] <- NA
Dist[diag(Dist)] <- NA
counts=compbypath(G,Hpath(1,N,Dist))
W=Weight(G)
#W[i,j]=0 #if we donot consider this relevance between sample i and sample j
C=counts$EC
WC=W$weight*C
WS=sum(WC[!is.na(WC)])
Wpermut(G,W$weight,WS)
Basic description
Description
Given the groups and the shortest Hamiltonian path, this function returns the number of edges that connect nodes between samples.
Usage
compbypath(G,re.path)
Arguments
G |
a list of all groups |
re.path |
the shortest Hamiltonian path returned from the function Hpath |
Value
the number of edges that connect nodes between samples
See Also
Hpath
Examples
d=100;n1=20;n2=30;n3=40;
N=n1+n2+n3
mu1=rep(0,d)
mu2=mu1
mu3=mu2+0.1
cov1=0.2^(abs(outer(1:d,1:d,"-")))
cov2=0.2^(abs(outer(1:d,1:d,"-")))
cov3=0.4^(abs(outer(1:d,1:d,"-")))
sam1=MASS::mvrnorm(n=n1,mu=mu1,Sigma=cov1)
sam2=MASS::mvrnorm(n=n2,mu=mu2,Sigma=cov2)
sam3=MASS::mvrnorm(n=n3,mu=mu3,Sigma=cov3)
Data=rbind(sam1,sam2,sam3)
Dist=philentropy::distance(Data, method = "euclidean")
Dist[lower.tri(Dist)] <- NA
Dist[diag(Dist)] <- NA
G=list()
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));G[[3]]=c((n1+n2+1):(n1+n2+n3));
compbypath(G,Hpath(1,N,Dist))
Basic description
Description
Calculates the shortest Hamiltonian path based on the sorted edge weights and the nodes
Usage
path.kruskal(nodes,edge_cost)
Arguments
nodes |
sequence of nodes 1,...,n from the graph which is based on the high-dimensional data that is provided by the reader |
edge_cost |
sorted edge weights |
Value
the shortest Hamiltonian path
See Also
Hpath
Examples
G=list()
set.seed(1)
n1=20;n2=40
N=n1+n2;
G[[1]]=c(1:n1);G[[2]]=c((n1+1):(n1+n2));
d=10
mu1=rep(0,d)
mu2=mu1+0.1
true.cov1=0.4^(abs(outer(1:d,1:d,"-")))
true.cov2=0.4^(abs(outer(1:d,1:d,"-")))
sam1=MASS::mvrnorm(n=n1,mu=mu1,Sigma=true.cov1)
sam2=MASS::mvrnorm(n=n2,mu=mu2,Sigma=true.cov2)
Data=rbind(sam1,sam2)
Dist=philentropy::distance(Data, method = "euclidean")
Dist[lower.tri(Dist)] <- NA
Dist[diag(Dist)] <- NA
mat=Dist
n1=1; n2=N; n0=n2-n1+1
edge.cost=matrix(NA,nrow=n0*(n0-1)/2,ncol=3)
temp=1;
for(i in n1:(n2-1))
for(j in (i+1):(n2))
{
edge.cost[temp,3]=mat[i,j];edge.cost[temp,1]=i-n1+1;edge.cost[temp,2]=j-n1+1;temp=temp+1;}
edge.cost=edge.cost[sort.list(edge.cost[,3]), ]
path.kruskal(c(1:n0),edge.cost)