ABSTRACT
The data in Table 14.1 are adapted from those given in Jackson (1991), and relate to hearing measurements with an instrument called an audiometer. An individual is exposed to a signal of a given frequency with an increasing intensity until the signal is perceived. The lowest intensity at which the signal is perceived is a measure of hearing loss, calibrated in units referred to as decibel loss in comparison with a reference standard for that particular instrument. Observations are obtained one ear at a time for a number of frequencies. In this example, the frequencies used were 500 Hz, 1000 Hz, 2000 Hz, and 4000 Hz. The limits of the instrument are −10 to 99 decibels. (A negative value does not imply better than average hearing; the audiometer had a calibration “zero”, and these observations are in relation to that.)
Principal component analysis is one of the oldest but still most widely used techniques of multivariate analysis. Originally introduced by Pearson (1901) and independently by Hotelling (1933), the basic idea of the method is to try to describe the variation of the variables in a set of multivariate data as parsimoniously as possible using a set of derived uncorrelated variables, each of which is a particular linear combination of those in the original data. In other words, principal component analysis is a transformation from the observed variables, y1i, . . . , ypi to new variables z1i, . . . , zpi where
z1i = a11y1i + a12y2i + · · · + a1pypi z2i = a21y1i + a22y2i + · · · + a2pypi ... =
... + ... +
... + ...
