library(MASS)
n <- 100
c <- vector('list', 7)
c[[1]] <- mvrnorm(n, mu = c( 0, 0), Sigma = rbind(c(2.0, 0.0), c( 0.0, 2.0)))
c[[2]] <- mvrnorm(n, mu = c( 0, 10), Sigma = rbind(c(2.0, -0.8), c(-0.8, 2.0)))
c[[3]] <- mvrnorm(n, mu = c(10, 0), Sigma = rbind(c(2.0, -0.8), c(-0.8, 2.0)))
c[[4]] <- mvrnorm(n, mu = c(-5, -5), Sigma = rbind(c(2.0, 0.8), c( 0.8, 2.0)))
c[[5]] <- mvrnorm(n, mu = c( 5, 5), Sigma = rbind(c(2.0, 0.8), c( 0.8, 2.0)))
c[[6]] <- mvrnorm(n, mu = c(-5, 5), Sigma = rbind(c(2.0, -0.8), c(-0.8, 2.0)))
c[[7]] <- mvrnorm(n, mu = c( 5, -5), Sigma = rbind(c(2.0, -0.8), c(-0.8, 2.0)))
for (i in seq_along(c))
{
c[[i]] <- as.data.frame(c[[i]])
colnames(c[[i]]) <- c('x', 'y')
}
d <- data.frame(c(rep(1, n), rep(0, n)), rbind(c[[1]], c[[5]]))
colnames(d) <- c('blue', 'x', 'y')
COL <- c(rgb(255, 0, 0, 105, max = 255), # 赤
rgb( 0, 0, 255, 105, max = 255), # 青
rgb( 0, 155, 0, 105, max = 255), # 緑
rgb(100, 100, 100, 20, max = 255)) # 灰
draw.fig <- function()
{
matplot (NA, type = 'n',
xlim = c(-10, 15), ylim = c(-10, 20),
xlab = 'x', ylab = 'y')
grid()
matlines(x = c[[1]]$x, y = c[[1]]$y, type = 'p', pch = 1, col = COL[2])
matlines(x = c[[5]]$x, y = c[[5]]$y, type = 'p', pch = 1, col = COL[1])
}
draw.fig()
legend('topright', col = COL[1:2], pch = c(1, 1), bg = 'white',
legend = c('赤', '青'))
library(e1071)
KERNEL <- c('linear', 'polynomial', 'sigmoid', 'radial')
k <- 1
cv <- tune('svm', as.factor(blue) ~ ., data = d,
kernel = KERNEL[k], type = 'C-classification',
ranges = list(
cost = 2^(-4:4)))
cv
##
## Parameter tuning of 'svm':
##
## - sampling method: 10-fold cross validation
##
## - best parameters:
## cost
## 0.5
##
## - best performance: 0.015
dx <- 0.2
dy <- 0.2
dgrid <- expand.grid(x = seq(-25, 25, dx),
y = seq(-25, 25, dy))
pred <- predict(cv$best.model, newdata = dgrid)
draw.fig()
sv <- d[cv$best.model$index, -1]
matpoints(x = sv[, 1], y = sv[, 2], pch = 16, cex = 0.5, col = 1)
dgrid.blue <- dgrid[pred == 1, ]
fill.cell <- function(x, y)
{
xline <- c(x - dx/2, x + dx/2)
ylow <- c(y - dy/2, y - dy/2)
yupp <- c(y + dy/2, y + dy/2)
polygon(c(xline, rev(xline)), c(ylow, yupp), border = F, col = COL[4])
}
for (i in 1:nrow(dgrid))
{
if (pred[i] == 1) fill.cell(dgrid$x[i], dgrid$y[i])
}
title(paste0('SVM（カーネル：', KERNEL[k], '）による分類'))
legend('topright', col = c(COL[1:2], 1, NA), pch = c(1, 1, 16, NA),
fill = c(NA, NA, NA, COL[4]), border = F, bg = 'white',
legend = c('赤（０）', '青（１）', 'サポートベクター', '青（１）と分類する範囲'))
matplot (NA, type = 'n', xlim = c(-10, 10), ylim = c(-10, 10),
xlab = 'x', ylab = 'y')
grid()
matlines(x = c[[1]]$x, y = c[[1]]$y, type = 'p', pch = 1, col = COL[2])
matlines(x = c[[4]]$x, y = c[[4]]$y, type = 'p', pch = 1, col = COL[1])
matlines(x = c[[5]]$x, y = c[[5]]$y, type = 'p', pch = 1, col = COL[1])
matlines(x = c[[6]]$x, y = c[[6]]$y, type = 'p', pch = 1, col = COL[1])
matlines(x = c[[7]]$x, y = c[[7]]$y, type = 'p', pch = 1, col = COL[1])
legend('topright', col = COL[1:2], pch = c(1, 1), bg = 'white',
legend = c('赤', '青'))
library(plot3D)
f <- function(x, y) x^2 + y^2
x.g <- seq(-50, 50, 5)
y.g <- seq(-50, 50, 5)
z.g <- outer(x.g, y.g, function(x, y) x*0 + y*0 + 10)
library(latex2exp)
#cairo_pdf('kernel_trick.pdf')
scatter3D(x = c[[1]]$x, y = c[[1]]$y, z = f(c[[1]]$x, c[[1]]$y),
pch = 16, col = COL[2], bty = 'f', ticktype = 'detailed',
theta = 45, phi = 15,
main = TeX('$z = x^2 + y^2'),
xlim = c(-10, 10),
ylim = c(-10, 10),
zlim = c(0, 100),
surf = list(x = x.g, y = y.g, z = z.g, facet = NA, border = 'green'))
scatter3D(x = c[[4]]$x, y = c[[4]]$y, z = f(c[[4]]$x, c[[4]]$y), pch = 16, col = COL[1], add = T)
scatter3D(x = c[[5]]$x, y = c[[5]]$y, z = f(c[[5]]$x, c[[5]]$y), pch = 16, col = COL[1], add = T)
scatter3D(x = c[[6]]$x, y = c[[6]]$y, z = f(c[[6]]$x, c[[6]]$y), pch = 16, col = COL[1], add = T)
scatter3D(x = c[[7]]$x, y = c[[7]]$y, z = f(c[[7]]$x, c[[7]]$y), pch = 16, col = COL[1], add = T)
KERNEL
## [1] "linear" "polynomial" "sigmoid" "radial"
d <- data.frame(c(rep(1, n*3), rep(0, n*4)),
rbind(c[[1]], c[[2]], c[[3]], c[[4]], c[[5]], c[[6]], c[[7]]))
colnames(d) <- c('blue', 'x', 'y')
head(d)
## blue x y
## 1 1 -0.1096850 0.95707875
## 2 1 0.7956401 -0.06520749
## 3 1 0.4742479 0.09616036
## 4 1 1.9114075 1.13302332
## 5 1 -1.3237573 -0.36516864
## 6 1 0.4336386 -0.25593169
matplot (NA, type = 'n',
xlim = c(-10, 15), ylim = c(-10, 20),
xlab = 'x', ylab = 'y')
grid()
d.red <- d[d$blue == 0, ] # 赤データ
d.blue <- d[d$blue == 1, ] # 青データ
matlines(x = d.red$x, y = d.red$y, type = 'p', pch = 1, col = COL[1])
matlines(x = d.blue$x, y = d.blue$y, type = 'p', pch = 1, col = COL[2])
legend('topright', col = COL[1:2], pch = c(1, 1), bg = 'white',
legend = c('赤', '青'))
