Factor Analysis geometrical interpretations

Canonical analysis achieves this geometric interpretation of the response surface by transforming the estimated polynomial model into a simpler form. The origin of the factor space is first translated to the stationary point of the estimated response surface, the point at which the partial derivatives of the response with respect to all of the factors are simultaneously equal to zero (see Section 10.5). The new factor... 

Most experiments have inherent in them a large number of variables. The experimenter usually ignores most of these variables, assuming on a subjective basis that they are not important. The problem has been stated by Thomas Auf der Heyde and Hans-Beat Biirgi as a twofold one First, how can we avoid subjectively carving up the data into two-dimensional subsets, i.e., how can all n variables be analyzed simultaneously in order to reveal correlations between them Second, how can the dimensionality of the problem be objectively reduced in order to interpret and visualize these correlations Two main methods are presently employed to try to resolve this problem. These methods are cluster analysis, which sorts the data into groups (clusters) so that the data can be classified, and factor analysis, which finds those variables (factors) that account most successfully for the sample variance, that is, the differences or similarities between the various sets of geometric data. 

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