From b40fbbb490445f68453079ab33a3fc495ccb6059 Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Sun, 20 Jun 2021 14:42:03 +0200 Subject: [PATCH] lab12 --- podsumowanie/README.md | 54 +++++++++++ podsumowanie/lab12/analiza.png | Bin 0 -> 109260 bytes podsumowanie/lab12/biplot.png | Bin 0 -> 41232 bytes podsumowanie/lab12/estymatory.png | Bin 0 -> 29048 bytes podsumowanie/lab12/ladunki.png | Bin 0 -> 29292 bytes podsumowanie/lab12/osypisko.png | Bin 0 -> 69338 bytes podsumowanie/lab12/wielowymiarowy.png | Bin 0 -> 91372 bytes testowe/pomocnicze.R | 132 ++++++++++++++++++++++++-- 8 files changed, 176 insertions(+), 10 deletions(-) create mode 100644 podsumowanie/lab12/analiza.png create mode 100644 podsumowanie/lab12/biplot.png create mode 100644 podsumowanie/lab12/estymatory.png create mode 100644 podsumowanie/lab12/ladunki.png create mode 100644 podsumowanie/lab12/osypisko.png create mode 100644 podsumowanie/lab12/wielowymiarowy.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index b3b7244..767ac2d 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -827,12 +827,66 @@ Zagadnienia: ### R +```r +# współczynnik korelacji -1 ujemnie; 0 brak korelacji; 1 dodatnio +cor.test(USArrests$Rape,USArrests$UrbanPop, method="pearson") + +# analiza składowych głównych +(pca_1 <- prcomp(~ Murder + Assault + Rape, data = USArrests, scale = TRUE)) +summary(pca_1) + +# wykres ładunków - wartość bezwzględna +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) + +# wykres osypiska +plot(pca_1) + +# średnia +pca_1$sdev^2 +mean(pca_1$sdev^2) + +# biplot +biplot(pca_1) + +# minimalne drzewo +install.packages("ape") +library(ape) +plot(mst(dist(scale(USArrests[, -3]))), x1 = pca_1$x[, 1], x2 = pca_1$x[, 2]) +``` ### Zagadnienia +- Analiza składowych głównych - jest techniką redukcji wymiaru. Jej celem jest znalezienie niewielkiej liczby składowych głównych, które wyjaśniają w maksymalnym stopniu całkowitą wariancję z próby p zmiennych pierwotnych. S - to estymator nieobciążony.
+![analiza](lab12/analiza.png) +- Ładunki - dokładniejszą interpretację składowych można uzyskać poprzez wyznaczenie tzw. macierzy ładunków czynnikowych (które są współczynnikami korelacji między i-tą zmienną i j-tą składową).
+![ladunki](lab12/ladunki.png) +- Ładunki czynnikowe - podobnie jak współczynniki zawarte w wektorze własnym, odzwierciedlają wpływ poszczególnych zmiennych na daną składową główną. + +- Wykres osypiska - wykres wariancji poszczególnych składowych głównych. Możemy odrzucić te dla których wartość jest mniejsza od 80% lub gdy wartości własne skłądowej głównej są mniejsze od średniej
+![osypisko](lab12/osypisko.png) + +- Biplot
+![biplot](lab12/biplot.png) + +- Można stworzyć minimalne drzewo rozpinające - graf którego wierzchołkami są obserwacje, dwa punkty są połączone jedną ścieżką, a suma krwędzi jest minimalna. Punkty połączone krawędziami powinny być blisko siebie + +- Model wielowymiarowy.
+![wielowymiarowy](lab12/wielowymiarowy.png) + +- Estymatory
+![estymatory](lab12/estymatory.png) + +- Kreska nad zmienną oznacza zazwyczaj średnią (przynajmniej na wikipedii) diff --git a/podsumowanie/lab12/analiza.png b/podsumowanie/lab12/analiza.png new file mode 100644 index 0000000000000000000000000000000000000000..b4f88d20ab8fbedb70064864fdbe460a1075b9d2 GIT binary patch literal 109260 zcmeFXWn3Lg);){__u%fqo#5_n!QCaeL-1h1-GVy_?he7-HMqOG^Kb6W%rkT6>-+KL z*XPiutGl{t*RHi!)!HEna^eWEIItifAPABYB1#}2;GrNOV8zgoz?FJf$5jvzEH4XT zVFgKHVIlDKcdt0Tcy62tkN2 zWJMG~5fniPcoCs^CE$v{ityg;b+Q%kSA*gUcEY?=aL7&DMAt16bNK8CA-dAS@Rf`AbsTN<}_Md@Eg&ITSsVd>Lu z3s15HGU0|JbPCZ9yX@$B96wn_EeE{rGFnO^q)$8BKo|+K4Coegh1jR$nHdQpBmEbe}#-Q^~ii z$2Ox#J+<`yvSYrNeOSRvoR4{wVepq}5WDxFL{6`}0R>{T7 z;JL3yw+K^puXKRb2aawvJw30lTxTQGZV;;LmlLYrqvRS@vtR^9L02wpi=W>GVcAT$ z>(gT5n>BM|Y$Jo)j^f`_wtvH-X-;>~iTx_^L6!Sba2uQ@3+@U8^IKpsCNz{FQH5=r zJHboslo5yo5$qkf9#Nb0J#VLdGX=c&!dJ307_l~@hcS-yV_iLDs44ar1=oy?U$)Kc zHXb63cOaVz`mjQ4tCfqnoiFB&Ag2aWYd#hf9W%HYw$R%353j3NtJ6M|3yeKhN$(%E 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