Principle Component Analysis

Principal component analysis is a method of statistical anal- ysis used to reduce the dimensionality of a dataset without loss of signif- icant information. Given a set of p random variables, X = (X1; : : :Xp)t , principal component analysis nds p linear combinations of X, called principal components (PCs). The rst principal component is chosen to have maximal variance, while each subsequent PC has the next largest variance and is uncorrelated with previous PCs. If the random vari- ables are highly correlated, then the rst few principal components will account for a large portion of the total variance, allowing for a reduc- tion in the dimension of the dataset. A key observation of principal components is that the variance of the PCs are the eigenvalues of the covariance matrix and that the eigenvectors make up the coe cients of the linear combination that transforms X