What technique maintains variance while compressing data?

The correct answer is Principal Component Analysis (PCA) because it is specifically designed to reduce the dimensionality of data while preserving as much variance as possible. PCA achieves this by identifying the directions (principal components) in which the data varies the most. By projecting the data onto these components, PCA compresses the dataset, allowing for reduced complexity without losing the important structural relationships within the data.

PCA effectively transforms the original set of variables into a smaller set of uncorrelated variables, keeping the majority of the variance intact in the lower-dimensional space. This makes it particularly useful in scenarios where maintaining the essential characteristics of the data is crucial.

In contrast, feature scaling is used to standardize the range of independent variables or features, which does not inherently compress data or maintain variance but rather prepares the data for analysis. Clustering analysis groups data points into clusters based on similarity, which may involve some level of compression but does not focus on maintaining variance. Data encoding refers to converting data from one format to another, which may also not prioritize variance retention or compression in the same way PCA does.