Dimensionality Reduction identifies new directions in the data that explain the most variation. These directions are called?

Dimensionality Reduction identifies new directions in the data that explain the most variation. These directions are called?

• A. Filters
• B. Principal Components
• C. Features
• D. Clusters

Answer: (B)

Principal components are the directions along which the data vary the most. In dimensionality reduction, PCA identifies these new axes that maximize the amount of variance captured when you project the data onto them. The first principal component points in the direction of greatest variance, the second is the next orthogonal direction with the most remaining variance, and so on. Because they are orthogonal, they are uncorrelated and provide a compact, informative representation of the data. These directions come from the eigenvectors of the data’s covariance matrix (or the singular vectors in SVD). Using the top principal components allows you to reduce dimensionality while preserving as much of the original structure as possible. The other terms don’t describe these variance-maximizing directions: filters are not the standard term for these axes, features are the original variables, and clusters refer to groupings of samples.

Principal components are the directions along which the data vary the most. In dimensionality reduction, PCA identifies these new axes that maximize the amount of variance captured when you project the data onto them. The first principal component points in the direction of greatest variance, the second is the next orthogonal direction with the most remaining variance, and so on. Because they are orthogonal, they are uncorrelated and provide a compact, informative representation of the data. These directions come from the eigenvectors of the data’s covariance matrix (or the singular vectors in SVD). Using the top principal components allows you to reduce dimensionality while preserving as much of the original structure as possible. The other terms don’t describe these variance-maximizing directions: filters are not the standard term for these axes, features are the original variables, and clusters refer to groupings of samples.