Principal Component Analysis (PCA) is a statistical technique used for dimensionality reduction while preserving as much variance as possible in the data. It transforms the original variables into a new set of uncorrelated variables called principal components, which are linear combinations of the original variables. The first principal component captures the maximum variance, followed by the second principal component, and so on.

PCA is particularly useful in situations where you have a large number of variables, as it helps to reduce the complexity of the data without losing significant information. This is especially important in machine learning and data analysis, where high-dimensional data can lead to overfitting and the “curse of dimensionality” ⁵.

To perform PCA, the data is typically standardized, and then the covariance matrix is computed. The eigenvalues and eigenvectors of this matrix are calculated to identify the principal components. The resulting components can then be used for further analysis or modeling ²⁴.

If you have more specific questions about PCA or its applications, feel free to ask!