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require(lolR) require(ggplot2) require(MASS) n=400 d=30 r=3
Data for this notebook will be n=400
examples of d=30
dimensions.
We first visualize the first 2
dimensions:
testdat <- lol.sims.cigar(n, d) X <- testdat$X Y <- testdat$Y data <- data.frame(x1=X[,1], x2=X[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Simulated Data")
Projecting with PCA to 3
dimensions and visualizing the first 2
:
result <- lol.project.pca(X, r) data <- data.frame(x1=result$Xr[,1], x2=result$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Projected Data using PCA")
Projecting with LDA to K-1=1
dimensions:
liney <- MASS::lda(result$Xr, Y) result <- predict(liney, result$Xr) lhat <- 1 - sum(result$class == Y)/length(Y) data <- data.frame(x1=result$x[,1], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, fill=y)) + geom_density(adjust=1.5, alpha=0.6) + xlab("$x_1$") + ylab("Density") + ggtitle(sprintf("PCA-LDA, L = %.2f", lhat))
We visualize the first 2
dimensions:
testdat <- lol.sims.rtrunk(n, d) X <- testdat$X Y <- testdat$Y data <- data.frame(x1=X[,1], x2=X[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Simulated Data")
Projecting with PCA to 3
dimensions and visualizing the first 2
:
result <- lol.project.pca(X, r) data <- data.frame(x1=result$Xr[,1], x2=result$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Projected Data using PCA")
Projecting with LDA to K-1=1
dimensions:
liney <- MASS::lda(result$Xr, Y) result <- predict(liney, result$Xr) lhat <- 1 - sum(result$class == Y)/length(Y) data <- data.frame(x1=result$x[,1], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, fill=y)) + geom_density(adjust=1.5, alpha=0.6) + xlab("x1") + ylab("Density") + ggtitle(sprintf("PCA-LDA, L = %.2f", lhat))
We visualize the first 2
dimensions:
testdat <- lol.sims.rtrunk(n, d, rotate=TRUE) X <- testdat$X Y <- testdat$Y data <- data.frame(x1=X[,1], x2=X[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Simulated Data")
Projecting with PCA to 3
dimensions and visualizing the first 2
:
result <- lol.project.pca(X, r) data <- data.frame(x1=result$Xr[,1], x2=result$Xr[,2], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, y=x2, color=y)) + geom_point() + xlab("x1") + ylab("x2") + ggtitle("Projected Data using PCA")
Projecting with LDA to K-1=1
dimensions:
liney <- MASS::lda(result$Xr, Y) result <- predict(liney, result$Xr) lhat <- 1 - sum(result$class == Y)/length(Y) data <- data.frame(x1=result$x[,1], y=Y) data$y <- factor(data$y) ggplot(data, aes(x=x1, fill=y)) + geom_density(adjust=1.5, alpha=0.6) + xlab("x1") + ylab("Density") + ggtitle(sprintf("PCA-LDA, L = %.2f", lhat))
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