Principal Component Analysis aims at finding the dimensions (principal component) that explain most of the variance in a dataset. Once these components are found, a principal component score is computed for each row and each principal component. Remember the example of the questionnaire data we discussed in the preceding section. These scores can be understood as summaries (combinations) of the attributes that compose the data frame.
PCA produces the principal components by computing the eigenvalues of the covariance matrix of a dataset. There is one eigenvalue for each row in the covariance matrix. The computation of eigenvectors is also required to compute the principal component scores. The eigenvalues and eigenvectors are computed using the following equation, where A is the covariance matrix of interest, I is the identity matrix, k is a positive integer, λ is the eigenvalue and v is the eigenvector:
What is important to understand for...