Principal component analysis (
PCA) is a statistical procedure that uses an
orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of
linearly uncorrelated variables called
principal components. The number of principal components is less than or equal to the number of original variables. This transformation is defined in such a way that the first principal component has the largest possible
variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is
orthogonal to the preceding components. The resulting vectors are an uncorrelated orthogonal basis set. The principal components are orthogonal because they are the
eigenvectors of the
covariance matrix, which is symmetric. PCA is sensitive to the relative scaling of the original variables.