R_LAB_LSED_MSR_TEXT/LSED_Lab_4.R at master · Samox1/R_LAB_LSED_MSR_TEXT · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
### LSED - Laboratorium 4

rm(list=ls())
library(MASS)

draw.data.gauss <- function(S1, S2, m1, m2, n1, n2) {

  X1 <- mvrnorm(n1, m1, S1)
  X2 <- mvrnorm(n2, m2, S2)

  X1 <- data.frame(X1); colnames(X1) <- c("x", "y")
  X2 <- data.frame(X2); colnames(X2) <- c("x", "y")

  X1$class <- 1; X2$class <- 2

  data <- rbind(X1, X2); data$class <- factor(data$class)

  return(data)
}

# Parametry danych z rozkladu Gaussa
S1 <- matrix(c(4, 2, 2, 4), 2, 2)
S2 <- matrix(c(4, 2, 2, 2), 2, 2)

m1 <- c(-1, -1)
m2 <- c(2, 2)

n1 <- 30
n2 <- 20

# Generowanie obserwacji
data <- draw.data.gauss(S1, S2, m1, m2, n1, n2)


# Prosta funkcja do wyznaczania przynale¿nosci
# metoda k-nn
find.knn <- function(class, M, k) {

  k.nodes <- order(M)[1:k]

  tab <- table(class[k.nodes])

  return(rownames(tab)[which.max(tab)])
}

# Macierz odleg³oœci
M <- as.matrix(dist(data[,1:2]))

# Klasyfikacja za pomoc¹ prostej funkcji
class.own <- sapply(1:nrow(data), function(i) find.knn(data$class, M[i,], 1))

library(class)

# Funkcja knn
class.knn <- knn(data[,1:2], data[,1:2], data$class, 1)

# Porównanie
table(class.knn, class.own)

# Rysowanie punktów
plot.data <- function(data) {

  cols <- c("blue", "orange")

  plot(data[,1:2], col = cols[data$class], cex = 2)
  text(data[,1:2], labels = 1:nrow(data), cex = 0.6)

}

# Rozpinanie siatki
xp <- seq(-10, 10, 0.1)
yp <- seq(-10, 10, 0.1)

gr <- expand.grid(x = xp, y = yp)

# Klasyfikacja na siatce za pomoc¹ prostej funkcji
gr.k <- sapply(1:nrow(gr), function(i) find.knn(data$class, sqrt((data$x-gr$x[i])^2 + (data$y - gr$y[i])^2), 1))

# Klasyfikacja na siatce za pomoc¹ funkcji knn
k1 <- knn(data[,1:2], gr, data$class, 1)

# Wykreœlanie punktów
plot.data(data)

# Granica klasyfikacyjna za pomoc¹ prostej funkcji
contour(xp, yp, matrix(gr.k == "1", length(xp)), add = T, levels = 0.5, lwd = 2, col = "blue")

# Granica za pomoc¹ funkcji knn
contour(xp, yp, matrix(k1 == "1", length(xp)), add = T, levels = 0.5, col = "orange", lty = 2, lwd = 2)


### Czêœæ 2 - Metoda C-NN ###

# Rysujemy punkty
plot.data(data)

# Uruchamiamy wstêpn¹ funkcjê
nodes.cond <- condense(data[,1:2], data$class)

# Zaznaczamy punkty
points(data[nodes.cond,1:2], cex = 3, col = "red", pch = 22, lwd = 2)

# Uruchamiamy drug¹ funkcjê
nodes.red <- reduce.nn(data[,1:2], nodes.cond, data$class)

# Rysujemy punkty od nowa i zaznaczamy je
plot.data(data)
points(data[nodes.red,1:2], cex = 3, col = "red", pch = 22, lwd = 2)

# Testujemy skutecznoœæ
table(data$class, knn(data[nodes.red,1:2], data[,1:2], data$class[nodes.red]))


### Czêœæ 3 - metoda K-NN dla wielu klas ###
rm(list=ls())

draw.data.gauss3 <- function(S1, S2, S3, m1, m2, m3, n1, n2, n3) {

  X1 <- mvrnorm(n1, m1, S1)
  X2 <- mvrnorm(n2, m2, S2)
  X3 <- mvrnorm(n3, m3, S3)

  X1 <- data.frame(X1); colnames(X1) <- c("x", "y")
  X2 <- data.frame(X2); colnames(X2) <- c("x", "y")
  X3 <- data.frame(X3); colnames(X3) <- c("x", "y")

  X1$class <- 1; X2$class <- 2; X3$class <- 3

  data <- rbind(X1, X2, X3); data$class <- factor(data$class)

  return(data)
}

S1 <- matrix(c(4, 2, 2, 4), 2, 2)
S2 <- matrix(c(4, 2, 2, 2), 2, 2)

m1 <- c(-1, -1)
m2 <- c(2, 2)
m3 <- c(-2, 2)

n1 <- 30
n2 <- 20
n3 <- 30

data <- draw.data.gauss3(S1, S2, S2, m1, m2, m3, n1, n2, n3)

xp <- with(data, seq(min(x), max(x), length = 50))
yp <- with(data, seq(min(y), max(y), length = 50))

gr <- expand.grid(x = xp, y = yp)

gr.knn <- knn(data[,1:2], gr, data$class, 1)
image(x = xp, y = yp, matrix(as.numeric(gr.knn), 50), xlab = "x", ylab = "y")
points(data[,1:2], col = data$class, pch = 19)

par(mfrow = c(2,2))

gr.knn <- knn(data[,1:2], gr, data$class, 1)
image(x = xp, y = yp, matrix(as.numeric(gr.knn), 50), xlab = "x", ylab = "y")
title("k=1")
points(data[,1:2], col = data$class, pch = 19)

gr.knn <- knn(data[,1:2], gr, data$class, 2)
image(x = xp, y = yp, matrix(as.numeric(gr.knn), 50), xlab = "x", ylab = "y")
title("k=2")
points(data[,1:2], col = data$class, pch = 19)

gr.knn <- knn(data[,1:2], gr, data$class, 3)
image(x = xp, y = yp, matrix(as.numeric(gr.knn), 50), xlab = "x", ylab = "y")
title("k=3")
points(data[,1:2], col = data$class, pch = 19)

gr.knn <- knn(data[,1:2], gr, data$class, 5)
image(x = xp, y = yp, matrix(as.numeric(gr.knn), 50), xlab = "x", ylab = "y")
title("k=5")
points(data[,1:2], col = data$class, pch = 19)