# Graphical Lasso

Graphical Lasso is one of the Correlation Analysis for Multi-Variable using the idea of Sparce Modeling. It is also called "GGM (Graphical Gaussian Model".

If it seems be no relationship, this method thinks 0 for the index of the relationship. This process leads the simple thinking.

## The Word, "Graphical Modeling", in Old Writings.

The isdea, "Use 0", is used in the old writings. And it is called "Graphical Modeling". In this method, 0 is used by hand not automatically.

And this method uses Partial Correlation. This process has the weakness that we cannot calculate the inverse-matrix.

Graphical Lasso realizes what old writings wanted.

## By R

If we use the sample data and sample coad bellow, we can draw the ghraphs below.

library(glasso)
library(igraph)
setwd("C:/Rtest")
DataM <- as.matrix(Data)
COR <- cor(DataM)
RHO <- 0.2 # The number to change sparse condition
GM1 <- glasso(COR,RHO)\$wi
GM1
write.csv(GM1, file = "GM.csv")
# To make data to draw the graph
diag(GM1) <- 0
GM2 <- abs(GM1)
GM2max <- max(GM2)
GM2max[GM2max==0] <- 1 # because this number is used as base
GM3 <- log10(GM2/GM2max*1000)*3 # To set the thickness of line.(Max becomes 9)
GM3[GM3==-Inf] <- 0
GM3[GM3<0] <- 0
rownames(GM3) <- rownames(COR)
colnames(GM3) <- colnames(COR)
GM4 <- graph.adjacency(GM3,weighted=T, mode = "undirected")
plot(GM4, edge.width=E(GM4)\$weight)

NEXT LiNGAM