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121 lines
2.7 KiB
Plaintext
121 lines
2.7 KiB
Plaintext
```{r}
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setwd('/Users/arthurdanjou/Workspace/studies/M1/Data Analysis/TP1')
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```
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# Part 1 - Analysis of the data
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```{r}
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x <- c(1, 2, 3, 4)
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mean(x)
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y <- x - mean(x)
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mean(y)
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t(y)
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sum(y^2)
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```
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```{r}
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T <- read.table("Temperature Data.csv", header = TRUE, sep = ";", dec = ",", row.names = 1)
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n <- nrow(T)
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g <- colMeans(T)
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Y <- as.matrix(T - rep(1, n) %*% t(g))
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Dp <- diag(1 / n, n)
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V <- t(Y) %*% Dp %*% Y
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eigen_values <- eigen(V)$values
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vectors <- eigen(V)$vectors
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total_inertia <- sum(eigen_values)
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inertia_one <- max(eigen_values) / sum(eigen_values)
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inertia_plan <- (eigen_values[1] + eigen_values[2]) / sum(eigen_values)
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P <- Y %*% vectors[, 1:2]
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plot(P, pch = 19, xlab = "PC1", ylab = "PC2")
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text(P, rownames(T), cex = 0.7, pos = 3)
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axis(1, -10:10, pos = 0, labels = F)
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axis(2, -5:5, pos = 0, labels = F)
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```
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```{r}
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France <- P %*% matrix(c(0, -1, 1, 0), 2, 2)
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plot(France, pch = 19, xlab = "PC1", ylab = "PC2")
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text(France, rownames(T), cex = 0.7, pos = 3)
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axis(1, -10:10, pos = 0, labels = F)
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axis(2, -5:5, pos = 0, labels = F)
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```
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```{r}
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results <- matrix(NA, nrow = n, ncol = 2)
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colnames(results) <- c("Quality of Representation (%)", "Contribution to Inertia (%)")
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rownames(results) <- rownames(T)
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for (i in 1:n) {
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yi <- Y[i,]
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norm_yi <- sqrt(sum(yi^2))
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qlt <- sum((yi %*% vectors[, 1:2])^2) / norm_yi^2 * 100
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ctr <- (P[i, 1]^2 / eigen_values[1]) / n * 100
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results[i,] <- c(qlt, ctr)
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}
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# Add the total row
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results <- rbind(results, colSums(results))
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rownames(results)[n + 1] <- "Total"
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results
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```
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# Part 2 - PCA with FactoMineR
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```{r}
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library(FactoMineR)
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T <- read.csv("Temperature Data.csv", header = TRUE, sep = ";", dec = ",", row.names = 1)
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summary(T)
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```
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```{r}
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T.pca <- PCA(T, graph = F)
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plot.PCA(T.pca, axes = c(1, 2), habillage = 1, choix = "ind")
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plot.PCA(T.pca, axes = c(1, 2), habillage = 1, choix = "var")
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print("Var coords")
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round(T.pca$var$coord[, 1:2], 2)
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print("Eigen values")
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round(T.pca$eig, 2)
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print("Ind dis")
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round(T.pca$ind$dist, 2)
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print("Ind contrib")
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round(T.pca$ind$contrib[, 1:2], 2)
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print("Var contrib")
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round(T.pca$var$contrib[, 1:2], 2)
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```
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## We add new values
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```{r}
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Amiens <- c(3.1, 3.8, 6.7, 9.5, 12.8, 15.8, 17.6, 17.6, 15.5, 11.1, 6.8, 4.2)
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T <- rbind(T, Amiens)
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row.names(T)[16] <- "Amiens"
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Moscow <- c(-9.2, -8, -2.5, 5.9, 12.8, 16.8, 18.4, 16.6, 11.2, 4.9, -1.5, -6.2)
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T <- rbind(T, Moscow)
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row.names(T)[17] <- "Moscow"
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Marrakech <- c(11.3, 12.8, 15.8, 18.1, 21.2, 24.7, 28.6, 28.6, 25, 20.9, 15.9, 12.1)
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T <- rbind(T, Marrakech)
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row.names(T)[18] <- "Marrakech"
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```
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## We redo the PCA
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```{r}
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T.pca <- PCA(T, ind.sup = 16:18, graph = F)
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plot.PCA(T.pca, axes = c(1, 2), habillage = 1, choix = "ind")
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plot.PCA(T.pca, axes = c(1, 2), habillage = 1, choix = "var")
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```
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