Introduction
PCA is a sophisticated statistical technique that is commonly used in data analysis and dimensionality reduction. With its seamless integration into R, a popular programming language for statistical computing, PCA becomes even more accessible to researchers, data scientists, and analysts.
In this article, we will delve into the world of PCA using R, studying its techniques, applications, and interpretation. By understanding and applying PCA in R, you will gain valuable insights, uncover hidden patterns, and simplify complex datasets.
Let's Practice ... !
# Example data
data <- matrix(c(2, 4, 3, 1, 5, 6, 4, 2, 6, 8, 7, 5), ncol = 2)
# Perform PCA
pca_result <- prcomp(data, scale = TRUE)
# Print the summary of PCA results
summary(pca_result)
# Plotting
plot(pca_result$x[,1], pca_result$x[,2], col = "blue", pch = 16, xlab = "PC1", ylab = "PC2", main = "PCA Plot")
# Variance explained by principal components
var_exp <- pca_result$sdev^2 / sum(pca_result$sdev^2)
# Print the variance explained by each principal component
cat("Variance Explained:\n")
cat(paste("PC", 1:length(var_exp), ": ", var_exp * 100, "%\n", sep = ""))
By running the code, you'll get this result:
In this example, we start with a sample dataset (data) consisting of two variables. The prcomp() function is used to perform PCA on the data, with the scale = TRUE argument standardizing the variables.
The summary() function is called to display a summary of the PCA results, including eigenvalues, proportion of variance explained, and cumulative proportion.
We then create a scatter plot using plot() to visualize the data in the PCA space. The x-values correspond to the scores on the first principal component (pca_result$x[,1]), and the y-values correspond to the scores on the second principal component (pca_result$x[,2]). The points are plotted in blue (col = "blue") with a dot marker (pch = 16). The x-axis label is set to "PC1", and the y-axis label is set to "PC2". The title of the plot is "PCA Plot".
Next, we calculate the variance explained by each principal component. The squared standard deviations (pca_result$sdev^2) are divided by the sum of squared standard deviations to obtain the variance explained by each component. The results are stored in the var_exp variable.
Finally, we print the variance explained by each principal component using cat() and paste(). The result shows the percentage of variance explained by each principal component.
By running this code, you will obtain a PCA plot, where each point represents a sample projected onto the first two principal components. The summary provides additional information about the eigenvalues and variance explained by each component.
Feel free to modify the example code with your own dataset. Good Luck !
-asb, founder of myresearchxpress
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