Estimate adjacency matrix for equivalent FLC distributions based on states

Description

This function estimates the adjacency matrix mathbf{A} of all pairwise equivalent FLC distributions given the states s_1, …, s_K. See Details below.

Usage

estimate_state_adj_matrix(states = NULL, FLCs = NULL, pdfs.FLC = NULL, alpha = NULL, 
    distance = function(f, g) return(mean(abs(f - g))))

Arguments

Value

A K \times K adjacency matrix with a trimmed version of exp(-distance) or p-values. If alpha!=NULL then it returns the thresholded 0/1 matrix. However, here 1 stands for equivalent, i.e. not rejecting. The matrix is obtained by checking for pval>alpha (rather than the usual pval<alpha).

Details and user-defined distance function

The (i,j)th element of the adjacency matrix is defined as

mathbf{A}_{ij} = distance(P(X mid s_i), P(X mid s_j)) = distance(f, g),

where distance is either

a metric

in the function space of pdfs f and g, or

a two sample test

for H_0: f=g, e.g. a Kolmogorov-Smirnov test (distance="KS").

Again we use a functional programming approach and allow the user to specify any valid distance/similarity function distance = function(f, g) return(...).

If distance="KS" the adjacency matrix contains p-values of a Kolmogorov-Smirnov test or the thresholded versions (if alpha!=NULL) - see Return for details.

Otherwise distance is an R function that takes as an input two vectors f and g (e.g. the wKDE estimates for two states), and returns a non-negative, real number to estimate their distance. Default is the L_1 distance distance = function(f, g) return(mean(abs(f-g))).

Examples

WW <- matrix(runif(10000), ncol = 10)
WW <- normalize(WW)
temp_flcs <- cbind(rnorm(nrow(WW)))
temp_pdfs.FLC <- estimate_LC_pdfs(temp_flcs, WW)
AA_ks <- estimate_state_adj_matrix(states = weight_matrix2states(WW), FLCs = temp_flcs, 
    distance = "KS")
AA_L1 <- estimate_state_adj_matrix(pdfs.FLC = temp_pdfs.FLC)

par(mfrow = c(1, 2), mar = c(1, 1, 2, 1))
image2(AA_ks, zlim = c(0, 1), legend = FALSE, main = "Kolmogorov-Smirnov")
image2(AA_L1, legend = FALSE, main = "L1 distance")

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LICORS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LICORS/estimate_state_adj_matrix.Rd_%03d_medium.png", width=480, height=480)
> ### Name: estimate_state_adj_matrix
> ### Title: Estimate adjacency matrix for equivalent FLC distributions based
> ###   on states
> ### Aliases: estimate_state_adj_matrix
> ### Keywords: distribution manip multivariate nonparametric
> 
> ### ** Examples
> 
> WW <- matrix(runif(10000), ncol = 10)
> WW <- normalize(WW)
> temp_flcs <- cbind(rnorm(nrow(WW)))
> temp_pdfs.FLC <- estimate_LC_pdfs(temp_flcs, WW)
> AA_ks <- estimate_state_adj_matrix(states = weight_matrix2states(WW), FLCs = temp_flcs, 
+     distance = "KS")
> AA_L1 <- estimate_state_adj_matrix(pdfs.FLC = temp_pdfs.FLC)
> 
> par(mfrow = c(1, 2), mar = c(1, 1, 2, 1))
> image2(AA_ks, zlim = c(0, 1), legend = FALSE, main = "Kolmogorov-Smirnov")
> image2(AA_L1, legend = FALSE, main = "L1 distance")
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>