PCA works by transforming the original data into a new coordinate system where the greatest variance by any projection of the data comes to lie on the first coordinate (the first principal component), the second greatest variance on the second coordinate, and so on. The steps typically involve:
1. Standardization: The data is standardized so that each variable contributes equally to the analysis. 2. Covariance Matrix Computation: A covariance matrix is computed to understand the correlations between variables. 3. Eigenvalue Decomposition: Eigenvalues and eigenvectors of the covariance matrix are calculated to determine the principal components. 4. Selection of Principal Components: The principal components are selected based on the variance they explain, often using a scree plot for visualization.
