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zeKZ2;kGG7li1tE~wn%lVeqOH;ZLeP!qVaIy`)Q4zUr#4oL6i~}s2;PQHC}V!Le!bO z8na*BVu4p-^0Lf+7FA}-nFDkD{!LqB*w6mExj-^MHHIC_r z3d`Sx{>3I+xNe?mShoKAfAd|Pd zyU=etv_NfMEa>0My+CPQ3*%@^d;v^8gvr}6_3af~uxl@ z3qSV)p2aw*1uV>0=UTw8acyCqCUf0baxJ|DyQ<81XfgfK`M}&ynfsImlUHZ$lg#zh zV2)RxTku1@Zed;2eSZdS2+<5)(67Oaqb5_2)~|&rMbtWf`S*L@Wz84-r(HGXeyGOe zm6>)~`>Zl^-82?({a^W^@82F{{6F6iQ1PPT{Rn>?V|-LfkjmfR?)*=Z_@5;4|7nu= Q>kXIx0jBBSdDb@o0P9s|rT_o{ literal 0 HcmV?d00001 diff --git a/zajecia12/.Rhistory b/zajecia12/.Rhistory new file mode 100644 index 0000000..ed2b76d --- /dev/null +++ b/zajecia12/.Rhistory @@ -0,0 +1,85 @@ +head(USArrests) +pairs(USArrests) +cor.test(USArrests$Murder,USArrests$UrbanPop, method="pearson") +cor.test(USArrests$Rape,USArrests$UrbanPop, method="pearson") +(pca_1 <- prcomp(~ Murder + Assault + Rape, data = USArrests, scale = TRUE)) +summary(pca_1) +head(pca_1$x) +cat("...") +pca_1$rotation +par(mfrow = c(1, 2)) +matplot(pca_1$rotation, type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = '�adunki', ylim = c(-0.9, 1.05), +xaxt = "n") +axis(1, at = 1:3, labels = rownames(pca_1$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3'), ncol = 3, col = 1:3, lwd = 2) +text(rep(1, 3), pca_1$rotation[1, ], round(pca_1$rotation[1, ], 2), pos = 4) +text(rep(2, 3), pca_1$rotation[2, ], round(pca_1$rotation[2, ], 2), pos = 1) +text(rep(3, 3), pca_1$rotation[3, ], round(pca_1$rotation[3, ], 2), pos = 2) +matplot(abs(pca_1$rotation), type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = '|�adunki|', ylim = c(0, 1.05), +xaxt = "n") +axis(1, at = 1:3, labels = rownames(pca_1$rotation)) +text(rep(1, 3), abs(pca_1$rotation)[1, ], abs(round(pca_1$rotation[1, ], 2)), pos = 4) +text(rep(2, 3), abs(pca_1$rotation)[2, ], abs(round(pca_1$rotation[2, ], 2)), pos = 1) +text(rep(3, 3), abs(pca_1$rotation)[3, ], abs(round(pca_1$rotation[3, ], 2)), pos = 2) +par(mfrow = c(1, 1)) +plot(pca_1) +# wartości własne = wariancje +pca_1$sdev^2 +mean(pca_1$sdev^2) +biplot(pca_1) +library(ape) +install.packages("ape") +library(ape) +plot(mst(dist(scale(USArrests[, -3]))), x1 = pca$x[, 1], x2 = pca$x[, 2]) +plot(mst(dist(scale(USArrests[, -3]))), x1 = pca_1$x[, 1], x2 = pca_1$x[, 2]) +mtcars_sel <- mtcars[, c(1, 3:7)] +(pca_2 <- prcomp(mtcars_sel, scale = TRUE)) +summary(pca_2) +head(pca_2$x) +cat("...") +pca_2$rotation +par(mfrow = c(2, 1)) +matplot(pca_2$rotation, type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = 'ładunki', ylim = c(-0.9, 1.05), +xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_2$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +matplot(abs(pca_2$rotation), type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = '|ładunki|', ylim = c(0, 1.05), +xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_2$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +par(mfrow = c(1, 1)) +plot(pca_2) +# trzecie podejście +# wartości własne = wariancje +pca_2$sdev^2 +mean(pca_2$sdev^2) +## 1, tak musi być przy skalowaniu +# Pomijamy te składowe główne, których wartości własne są mniejsze od średniej. +# Zatem wybieramy dwie. +biplot(pca_2) +plot(mst(dist(mtcars_sel)), x1 = pca_2$x[, 1], x2 = pca_2$x[, 2]) +(pca_3 <- prcomp(mtcars_sel, scale = FALSE, center = FALSE)) +summary(pca_3) +head(pca_3$x) +cat("...") +pca_3$rotation +par(mfrow = c(2, 1)) +matplot(pca_3$rotation, type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = '�adunki', ylim = c(-0.9, 1.15), +xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_3$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +matplot(abs(pca_3$rotation), type = 'l', lty = 1, lwd = 2, +xlab = 'zmienne', ylab = '|�adunki|', ylim = c(0, 1.1), +xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_3$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +par(mfrow = c(1, 1)) +plot(pca_3) +#1 +pca_3$sdev^2 +mean(pca_3$sdev^2) diff --git a/zajecia12/README.md b/zajecia12/README.md new file mode 100644 index 0000000..f65a454 --- /dev/null +++ b/zajecia12/README.md @@ -0,0 +1,8 @@ +# Zajęcia 12 +Analiza składowych głównych + + +## Notatki + - ładunki - Dokładniejszą interpretację składowych można uzyskać poprzez wyznaczenie tzw. macierzy ładunków czynnikowych (które są współczynnikami korelacji między i-tą zmienną i j-tą składową). + +- Ładunki czynnikowe, podobnie jak współczynniki zawarte w wektorze własnym, odzwierciedlają wpływ poszczególnych zmiennych na daną składową główną. \ No newline at end of file diff --git a/zajecia12/Zajęcia12.pdf b/zajecia12/Zajęcia12.pdf new file mode 100644 index 0000000000000000000000000000000000000000..44ccb90cd15cbc72d43048603bb4a16755e16af8 GIT binary patch literal 1609366 zcmV)3K+C@+P((&8F)lX>3N#=vAa7!73OqatFGgu>bY*fNFGg%(bY(Vma%Ev{3V59Dy~%Rqunr}<_gB=qBjlhcilRQ_t@;CQ#Ou3A 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/dev/null +++ b/zajecia12/zadania.R @@ -0,0 +1,123 @@ +#ZAD1 +head(USArrests) +pairs(USArrests) +#UrbanPop jest najsłabiej skorelowana z pozostałymi +cor.test(USArrests$Murder,USArrests$UrbanPop, method="pearson") +cor.test(USArrests$Rape,USArrests$UrbanPop, method="pearson") + +(pca_1 <- prcomp(~ Murder + Assault + Rape, data = USArrests, scale = TRUE)) + +summary(pca_1) + +head(pca_1$x) +cat("...") + +pca_1$rotation +par(mfrow = c(1, 2)) +matplot(pca_1$rotation, type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = 'ładunki', ylim = c(-0.9, 1.05), + xaxt = "n") +axis(1, at = 1:3, labels = rownames(pca_1$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3'), ncol = 3, col = 1:3, lwd = 2) +text(rep(1, 3), pca_1$rotation[1, ], round(pca_1$rotation[1, ], 2), pos = 4) +text(rep(2, 3), pca_1$rotation[2, ], round(pca_1$rotation[2, ], 2), pos = 1) +text(rep(3, 3), pca_1$rotation[3, ], round(pca_1$rotation[3, ], 2), pos = 2) +matplot(abs(pca_1$rotation), type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = '|ładunki|', ylim = c(0, 1.05), + xaxt = "n") +axis(1, at = 1:3, labels = rownames(pca_1$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3'), ncol = 3, col = 1:3, lwd = 2) +text(rep(1, 3), abs(pca_1$rotation)[1, ], abs(round(pca_1$rotation[1, ], 2)), pos = 4) +text(rep(2, 3), abs(pca_1$rotation)[2, ], abs(round(pca_1$rotation[2, ], 2)), pos = 1) +text(rep(3, 3), abs(pca_1$rotation)[3, ], abs(round(pca_1$rotation[3, ], 2)), pos = 2) +par(mfrow = c(1, 1)) + +plot(pca_1) + +# trzecie podejście +# wartości własne = wariancje +pca_1$sdev^2 +mean(pca_1$sdev^2) +## 1, tak musi być przy skalowaniu +# Pomijamy te składowe główne, których wartości własne są mniejsze od średniej. +# Zatem wybieramy jedną. + +biplot(pca_1) + +install.packages("ape") +library(ape) +plot(mst(dist(scale(USArrests[, -3]))), x1 = pca_1$x[, 1], x2 = pca_1$x[, 2]) + +#ZAD2 + +mtcars_sel <- mtcars[, c(1, 3:7)] +(pca_2 <- prcomp(mtcars_sel, scale = TRUE)) + +summary(pca_2) + +head(pca_2$x) +cat("...") + +pca_2$rotation +par(mfrow = c(2, 1)) +matplot(pca_2$rotation, type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = 'ładunki', ylim = c(-0.9, 1.05), + xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_2$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +matplot(abs(pca_2$rotation), type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = '|ładunki|', ylim = c(0, 1.05), + xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_2$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +par(mfrow = c(1, 1)) + +plot(pca_2) + +# trzecie podejście +# wartości własne = wariancje +pca_2$sdev^2 +mean(pca_2$sdev^2) +## 1, tak musi być przy skalowaniu +# Pomijamy te składowe główne, których wartości własne są mniejsze od średniej. +# Zatem wybieramy dwie. + +biplot(pca_2) + +library(ape) +plot(mst(dist(mtcars_sel)), x1 = pca_2$x[, 1], x2 = pca_2$x[, 2]) + + +(pca_3 <- prcomp(mtcars_sel, scale = FALSE, center = FALSE)) + +summary(pca_3) + +head(pca_3$x) +cat("...") + +pca_3$rotation +par(mfrow = c(2, 1)) +matplot(pca_3$rotation, type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = '�adunki', ylim = c(-0.9, 1.15), + xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_3$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +matplot(abs(pca_3$rotation), type = 'l', lty = 1, lwd = 2, + xlab = 'zmienne', ylab = '|�adunki|', ylim = c(0, 1.1), + xaxt = "n") +axis(1, at = 1:6, labels = rownames(pca_3$rotation)) +legend('topleft', legend = c('PC1', 'PC2', 'PC3', 'PC4', 'PC5', 'PC6'), ncol = 6, col = 1:6, lwd = 2) +par(mfrow = c(1, 1)) + + +plot(pca_3) +#1 + +pca_3$sdev^2 +mean(pca_3$sdev^2) + + + + + + diff --git a/zajecia12/zajecia12.Rproj b/zajecia12/zajecia12.Rproj new file mode 100644 index 0000000..8e3c2eb --- /dev/null +++ b/zajecia12/zajecia12.Rproj @@ -0,0 +1,13 @@ +Version: 1.0 + +RestoreWorkspace: Default +SaveWorkspace: Default +AlwaysSaveHistory: Default + +EnableCodeIndexing: Yes +UseSpacesForTab: Yes +NumSpacesForTab: 2 +Encoding: UTF-8 + +RnwWeave: Sweave +LaTeX: pdfLaTeX