A government agency is conducting a national census to assess program needs by area and...

The primary requirement is dimensionality reduction on high-dimensional structured data to uncover hidden patterns. Principal Component Analysis (PCA) is a linear dimensionality reduction technique specifically designed for this purpose and is available as a built-in algorithm in Amazon SageMaker.

PCA transforms the original features into a smaller set of orthogonal components that preserve the maximum possible variance. This makes PCA ideal for large tabular datasets such as census data, where hundreds of correlated variables are common.

t-SNE (Option B) is mainly used for visualization in very low dimensions (2D or 3D) and does not scale well for large datasets or production analysis. k-means (Option C) is a clustering algorithm, not a dimensionality reduction method. Random Cut Forest (Option D) is used for anomaly detection.

Therefore, PCA is the correct and AWS-recommended solution.