In this edition of our dimensionality reduction course, we'll explore a side-by-side comparison of Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). Our journey will include identifying contexts in which PCA and LDA excel, examining real-world scenarios where LDA is particularly beneficial, and working through an R script that performs LDA and PCA on the famous Iris dataset.

PCA and LDA are essential tools for reducing the dimensionality of high-dimensional data, each using a distinct methodology. PCA is an unsupervised technique that transforms a set of features into linearly uncorrelated principal components based on maximum variance. In contrast, LDA is a supervised method that seeks to maximize the separability between data classes.

The choice between PCA and LDA depends on the dataset and the problem at hand. PCA is ideal for larger datasets with unreliable or missing class labels, while LDA is best suited for smaller, well-labeled datasets with low within-class and high between-class variability.

LDA's ability to maintain class separability during dimensionality reduction makes it valuable in many domains, including image recognition, customer segmentation in marketing, disease detection in healthcare, and protein analysis in bioinformatics.

Let's now walk through an R script that applies LDA and PCA to the Iris dataset, using R libraries such as MASS and caret. We'll break down the script step by step for clarity.

The Iris dataset is included in base R, so we can load it directly:

Standardizing features is a common requirement for many machine learning algorithms. We'll use the scale() function to standardize the numeric columns:

We'll use the caret package to split the data into training (60%) and testing (40%) sets:

We'll use the MASS package to perform LDA:

We'll use logistic regression (multinomial) from the nnet package to classify the species of Iris:

When applying PCA, it's important to decide how many principal components (PCs) to retain. In our example, we selected the first two principal components ([, 1:2]) for simplicity and visualization purposes. However, in practice, the number of PCs is often chosen based on the proportion of variance explained. You can examine the variance explained by each component using the summary() function on the PCA model:

Typically, you would select enough PCs to capture a desired threshold of total variance (e.g., 90% or 95%). For this lesson, we used two PCs to illustrate the process, but you should adjust this number based on your specific dataset and analysis goals.

You can adjust the number of principal components used by changing the column selection (e.g., [, 1:3] for three PCs), ideally based on the cumulative variance explained.

In this lesson, we compared PCA and LDA, discussed scenarios for choosing one over the other, explored real-world applications of LDA, and implemented both PCA and LDA using R and the Iris dataset. In the upcoming practical sessions, you will gain further hands-on experience applying PCA and LDA to various datasets using R, deepening your understanding of these powerful dimensionality reduction techniques. Let's move ahead!