Which technique reduces dimensionality by projecting data onto principal components?

Which technique reduces dimensionality by projecting data onto principal components?

• A. Autoencoders
• B. RNNs
• C. CNNs
• D. PCA

Answer: (D)

Dimensionality reduction by projecting data onto the directions that capture the most variance is achieved with Principal Component Analysis. PCA finds the eigenvectors of the data’s covariance matrix, called principal components, which are orthogonal directions arranged by how much variance they explain. By selecting the top k components and projecting the data onto the subspace they span, you get a lower-dimensional representation that retains as much of the original variability as possible. This projection is linear and unsupervised, and the components represent the main axes of variation in the data. Autoencoders can reduce dimensionality via learned representations, but they aren’t restricted to projecting onto principal components and can encode nonlinear structure. RNNs and CNNs are neural architectures for sequences and images, not methods focused on projecting onto principal components for dimensionality reduction.

Dimensionality reduction by projecting data onto the directions that capture the most variance is achieved with Principal Component Analysis. PCA finds the eigenvectors of the data’s covariance matrix, called principal components, which are orthogonal directions arranged by how much variance they explain. By selecting the top k components and projecting the data onto the subspace they span, you get a lower-dimensional representation that retains as much of the original variability as possible. This projection is linear and unsupervised, and the components represent the main axes of variation in the data.

Autoencoders can reduce dimensionality via learned representations, but they aren’t restricted to projecting onto principal components and can encode nonlinear structure. RNNs and CNNs are neural architectures for sequences and images, not methods focused on projecting onto principal components for dimensionality reduction.