Deep Learning の次は、TDA 「トポロジカル・データ・アナリシス」 (Topological data analysis) が来る ? ～ その概要と、R言語 / Python言語 実装ライブラリ をちらっと調べてみた ref: http://qiita.com/HirofumiYashima/items/b07483af7ef31c30dacc

bash

wget https://pypi.python.org/packages/source/f/fastcluster/fastcluster-1.1.13.tar.gz
tar -xf fastcluster-1.1.13.tar.gz
cd fastcluster-1.1.13
python setup.py install --user
cd ..
rm fastcluster-1.1.13.tar.gz
rm -r fastcluster-1.1.13/

file0.txt

install.packages("TDA")
library(MASS)
library(TDA)

#データの生成
mu1 <- c(0, 0)
Sigma1 <- matrix(c(1, 0.3, 0.3, 1), 2, 2)
x1 <- mvrnorm(30, mu1, Sigma1)
mu2 <- c(8, 0)
Sigma2 <- matrix(c(1, -0.2, -0.2, 1), 2, 2)
x2 <- mvrnorm(30, mu2, Sigma2)
mu3 <- c(4, 6)
Sigma3 <- matrix(c(1, 0, 0, 1), 2, 2)
x3 <- mvrnorm(30, mu3, Sigma3)
x <- rbind(x1,x2,x3)

#TDAによる計算
Diag <- ripsDiag(X = x, maxdimension = 0, maxscale = 5, library = "Dionysus")

#可視化（バーコードプロット）
D <- Diag[["diagram"]]
n <- nrow(D)
plot(c(min(D[,2]), max(D[,3])-1.5), c(1,n + 1), type="n", xlab = "radius", ylab ="", xlim=c(min(D[,2]), max(D[,3])-1.5), ylim=c(1, n + 1), yaxt ='n')
segments(D[,2], 1:n, sort(D[,3]), 1:n, lwd=2)

file1.txt

library(TDA)

#データの生成
image_A <- cbind(x= c(0,1,2,3,4,5,6,7,8,9,10,3.5,5,6.5) * 0.6 + 2,
y =c(0,3,6,9,12,15,12,9,6,3,0,6,6,6)*0.55 + 1.25)
image_L <- cbind(x = c(0,0,0,0,0,0,0,0,0,1,0.25,0.5,0.75,1.25,1.5) * 4 + 2 ,
y = c(0,1,2,3,4,5,6,7,8,0,0,0,0,0,0) + 1.25)
image_B <- cbind(x = c(0,0,0,0,0,0,0,0,0,1,1,1,1.25,1.25,1.5,1.5,1.5,0.25,0.25,0.25,0.5,0.5,0.5,0.75,0.75,0.75,1.25,1.25) * 4 +2,
y = c(0,1,2,3,4,5,6,7,8,0,4,8,5.3,6.6,1,2,3,0,4,8,0,4,8,0,4,8,3.5,0.5) + 1.25)

#TDAによる計算
Diag_A <- ripsDiag(X = image_A,maxdimension = 1,maxscale = 5)
Diag_L <- ripsDiag(X = image_L,maxdimension = 1,maxscale = 5)
Diag_B <- ripsDiag(X = image_B,maxdimension = 1,maxscale = 5)

#可視化（パーシステント図）
plot(Diag_A$diagram)
plot(Diag_L$diagram)
plot(Diag_B$diagram)

Python

easy_install --upgrade --user fastcluster