In PCA, what is the purpose of selecting the top eigenvectors?

• A. To maximize correlation between components.
• B. To normalize the data.
• C. To capture the directions of greatest variance in the data.
• D. To compute the mean.

Answer: (C)

PCA is about finding directions in which the data varies the most. When you look at the covariance structure of the data, each eigenvector points along a direction in feature space, and its eigenvalue tells you how much variance lies along that direction. The top eigenvectors correspond to the largest eigenvalues, meaning they capture the greatest amount of variance. By projecting the data onto these leading directions, you retain as much information as possible while reducing dimensionality. That’s why selecting the top eigenvectors serves to capture the directions of greatest variance in the data.

For context, normalizing the data is a preprocessing step you often do before PCA to ensure features are on comparable scales, and computing the mean is part of centering the data, not the purpose of choosing eigenvectors. PCA also yields uncorrelated components, rather than maximizing correlation.