Which technique is commonly used to reduce high-dimensional data into low-dimensional data while preserving information for prediction?

Principal Component Analysis (PCA) is a widely used technique for reducing the dimensionality of high-dimensional data while preserving as much information as possible. The method achieves this by transforming the original dataset into a new coordinate system where the greatest variances by any projection of the data lie on the first coordinates, known as principal components. This transformation helps to identify the directions (axes) in which the data varies the most and allows us to reduce dimensions effectively while retaining significant information for predictive tasks.

PCA is particularly useful in scenarios where the number of features is large relative to the number of observations, which can lead to issues such as overfitting and increased computational costs. By compressing the data down to its principal components, PCA can significantly enhance the efficiency of subsequent machine learning algorithms without sacrificing the integrity of the underlying patterns in the data.

In contrast, linear regression focuses on modeling relationships between dependent and independent variables but does not inherently address dimensionality reduction. Support Vector Machines (SVMs) are primarily used for classification tasks and may also involve kernel transformations but do not specifically target dimensionality reduction. k-Means clustering is a clustering technique that groups data points into k clusters based on feature similarity and is more concerned with partitioning the data rather than reducing