1 Data Analysis  Data Matrix Variables ObjectsX1X1 X2X2 X3X3 …XPXP n

2 Two Approaches  R-techniques -Comparing columns of the data matrix, i.e., the variables -Principal Component Analysis, Factor Analysis

3  Q-techniques -Comparing the rows of the data matrix, i.e., the different objects -Discriminant Analysis, Cluster Analysis, Multidimensional Scaling

4 Geometrical Ideas  R-techniques -The columns can be viewed as p points in a n- dimensional space, called Objects Space (or R space). -The interpretation of the correlation matrix r ij in the object space for the centered data matrix Y.

5  Q-techniques -The n rows can be viewed as n points in p- dimensional Q-space or variable space. -Look at the Euclidean distance between two rows, and