Principal Component Analysis

Principal component analysis is a one-sample technique applied to data with no groupings among the observations and no partitioning of the variables into subvectors y and x. Principal components are concerned only with the core structure of a single sample of observations on p variables. In principal component analysis, we seek to maximize the variance of a linear combination of the variables. For example, the first principal component could be used to rank students on the basis of their scores on achievement tests in English, mathematics, reading, and so on. An average score would provide a single scale on which to compare the students, but with unequal weights in the principal component, we can spread the…