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| 1 | +### LSED - LAB nr 10 |
| 2 | + |
| 3 | +rm(list=ls()) |
| 4 | +library(MASS) |
| 5 | + |
| 6 | + |
| 7 | +### --- ANALIZA SK£ADOWYCH G£OWNYCH --- ### |
| 8 | + |
| 9 | + |
| 10 | +# Zale¿noœæ y = x |
| 11 | +x <- seq(-5, 5, by=.1) |
| 12 | +y <- x |
| 13 | + |
| 14 | +# Dodanie szumu |
| 15 | +eta <- runif(101, 0, 1) |
| 16 | +dzeta <- runif(101, 0, 1) |
| 17 | + |
| 18 | +x <- x + eta |
| 19 | +y <- y + dzeta |
| 20 | + |
| 21 | +# Wykres |
| 22 | +plot(x, y, pch=19, xlab="Test 1", ylab="Test 2", font=2, font.lab=2, xlim=c(-5,5), ylim=c(-5,5), asp = 1) |
| 23 | +abline(h=0, v=0, lwd=2, col="gray") |
| 24 | +abline(0,1,lwd=2,col="red") |
| 25 | +abline(0,-1,lwd=2,col="green") |
| 26 | +text(4.5,-0.5,expression(x[1]),cex=2) |
| 27 | +text(-0.5,4.5,expression(x[2]),cex=2) |
| 28 | +text(4.7,4,expression(y[1]),cex=2, col="red") |
| 29 | +text(-4.5,4,expression(y[2]),cex=2, col="green") |
| 30 | +title("Dane", cex.main=1.4) |
| 31 | + |
| 32 | + |
| 33 | +# Zapisanie wspolrzednych x i y |
| 34 | +# do struktury dataframe |
| 35 | + |
| 36 | +test <- data.frame(x, y) |
| 37 | + |
| 38 | +# Macierz kowariancji |
| 39 | +S <- cov(test) |
| 40 | + |
| 41 | +# Macierz korelacji |
| 42 | +Sc <- cor(test) |
| 43 | + |
| 44 | +# Wyznaczenie wartoœci i wektorów w³asnych |
| 45 | +eS <- eigen(S) |
| 46 | +eSc <- eigen(Sc) |
| 47 | + |
| 48 | +print(eS) |
| 49 | +print(eSc) |
| 50 | + |
| 51 | + |
| 52 | +# Wykonanie analizy sk³adowych glownych |
| 53 | +test.pc <- princomp(~., cor=T, data=test) |
| 54 | + |
| 55 | +# Wykreœlenie wariancji zwiaz¹nych ze sk³adowymi |
| 56 | +plot(test.pc, main="") |
| 57 | +title("Wariancja", cex.main=1.4) |
| 58 | + |
| 59 | +print(test.pc$sdev^2) |
| 60 | + |
| 61 | +# Wykres we wspó³rzêdnych sk³adowych g³ównych |
| 62 | +plot(test.pc$scores, xlim=c(-2,2), ylim=c(-2,2), xlab="Sk³adowa 1", ylab="Sk³adowa 2") |
| 63 | +title("Sk³adowe", cex.main=1.4) |
| 64 | + |
| 65 | + |
| 66 | +### --- NIELINIOWA ANALIZA SK£ADOWYCH G£OWNYCH --- ### |
| 67 | + |
| 68 | +# Dane irysów |
| 69 | +data(iris) |
| 70 | + |
| 71 | +# Liniowe PCA |
| 72 | +iris.pca <- princomp(~ ., data = iris[,-5], cor = TRUE) |
| 73 | +plot(iris.pca$scores, pch = 19, col = as.factor(iris[,5]), xlab="Sk³adowa 1", ylab="Sk³adowa 2") |
| 74 | + |
| 75 | + |
| 76 | +library(kernlab) |
| 77 | + |
| 78 | +# PCA nieliniowe z j¹drem radialnym |
| 79 | +iris.kpca <- kpca(~ ., data=iris[,-5], kernel="rbfdot", kpar = list(sigma=0.1)) |
| 80 | +plot(rotated(iris.kpca), pch = 19, col = as.factor(iris[,5]), xlab = "Sk³adowa 1", ylab = "Sk³adowa 2") |
| 81 | + |
| 82 | + |
| 83 | +### --- NIELINIOWA ANALIZA SK£ADOWYCH G£OWNYCH --- ### |
| 84 | + |
| 85 | +# MDS dla miast Europy |
| 86 | +euro.cmd = cmdscale(eurodist, k = 2) |
| 87 | + |
| 88 | +# Tworzenie rysunku |
| 89 | +plot(euro.cmd[,1], euro.cmd[,2], type = "n", xlab = "", ylab = "", axes = FALSE, main = "MDS Europa") |
| 90 | +text(euro.cmd[,1], euro.cmd[,2], labels(eurodist), cex = 0.9, xpd = TRUE) |
| 91 | + |
| 92 | +# Dane dotycz¹ce g³osowañ na prezydenta w stanach USA |
| 93 | +votes.repub <- cluster::votes.repub |
| 94 | + |
| 95 | +# Pozbywamy siê wartoœci NA |
| 96 | +dates <- c(1:15) |
| 97 | +ind <- apply(is.na(votes.repub[,-dates]), 1, any) |
| 98 | +votes <- votes.repub[!ind, -dates] |
| 99 | + |
| 100 | +votes.cmd <- cmdscale(dist(votes)) |
| 101 | + |
| 102 | +plot(votes.cmd, type = "n", xlab = "", ylab = "", axes = FALSE, main = "Stany USA w wyborach prezydenckich") |
| 103 | +text(votes.cmd, labels = rownames(votes.cmd), cex = 0.9, xpd = TRUE) |
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