Which technique reduces many correlated variables to a smaller number of uncorrelated components that capture most of the information?

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Multiple Choice

Which technique reduces many correlated variables to a smaller number of uncorrelated components that capture most of the information?

This question tests dimensionality reduction through a method that turns many correlated variables into a smaller set of uncorrelated components that still capture most of the information. Principal Components Analysis does this by forming new variables—principal components—that are linear combinations of the original ones. These components are constructed to be orthogonal (uncorrelated) and are ordered by how much variance they explain in the data. The first few components carry the majority of the information, so you can represent the data with fewer dimensions while reducing redundancy from correlations. The other options aren’t about reducing variables into informative components. Orthogonality is the property PCA achieves for its components, not a standalone technique. Data clustering and partitional clustering group observations into clusters and don’t reduce the number of variables or transform them into informative components.

This question tests dimensionality reduction through a method that turns many correlated variables into a smaller set of uncorrelated components that still capture most of the information. Principal Components Analysis does this by forming new variables—principal components—that are linear combinations of the original ones. These components are constructed to be orthogonal (uncorrelated) and are ordered by how much variance they explain in the data. The first few components carry the majority of the information, so you can represent the data with fewer dimensions while reducing redundancy from correlations.

The other options aren’t about reducing variables into informative components. Orthogonality is the property PCA achieves for its components, not a standalone technique. Data clustering and partitional clustering group observations into clusters and don’t reduce the number of variables or transform them into informative components.

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