What dimensionality reduction technique transforms data into uncorrelated variables capturing variance?

The dimensionality reduction technique that transforms data into uncorrelated variables while capturing maximum variance is Principal Component Analysis (PCA). PCA operates by identifying the directions (or principal components) in which the data varies the most.

In performing PCA, the original correlated features are converted into a new set of uncorrelated features, which are linear combinations of the original variables. This is achieved by using eigenvalue decomposition or singular value decomposition on the covariance matrix of the data. The principal components are arranged in order of the amount of variance they capture, allowing for the selection of the top components that retain the most significant variations present in the dataset. This is particularly useful for reducing the dimensionality of the data, while still maintaining key characteristics.

Other options present techniques that serve different purposes. Factor Analysis focuses more on identifying underlying relationships between variables and is often used in the context of latent variable modeling. Dimensionality Reduction is a general term that encompasses various techniques, but it does not specify a method. Cluster Analysis is aimed at grouping similar data points together rather than transforming the data into a new representation of uncorrelated variables.