ABSTRACT
In all the examples and analyses presented so far, we have dealt with the analysis of the rows of a table, visualizing the row profiles and using the columns as reference points for the interpretation: let’s call this the “row analysis”. All this can be applied in a completely symmetric way to the columns of the same table. This can be thought of as transposing the table, making the columns the rows and vice versa, and then repeating all the procedures described in Chapters 2 to 7. In this chapter we shall show that the row analysis and column analysis are intimately connected. In fact, if a row analysis is performed, then the column analysis is actually being performed as well, and vice versa. CA can thus be regarded as the simultaneous analysis of the rows and columns.
Summary of row analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Column analysis — profile values have symmetric interpretation . . . . 58 Column analysis — same total inertia . . . . . . . . . . . . . . . . . . . 58 Column analysis — same dimensionality . . . . . . . . . . . . . . . . . . 58 Column analysis — same low-dimensional approximation . . . . . . . . 59 Column analysis — same coordinate values, rescaled . . . . . . . . . . . 59 Principal axes and principal inertias . . . . . . . . . . . . . . . . . . . . 60 Scaling factor is the square root of the principal inertia . . . . . . . . . 60 Correlation interpretation of the principal inertia . . . . . . . . . . . . . 61 Graph of the correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Principal coordinates and standard coordinates . . . . . . . . . . . . . . 62 Maximizing squared correlation with the average . . . . . . . . . . . . . 63 Minimizing loss of homogeneity within variables . . . . . . . . . . . . . 63 SUMMARY: Symmetry of Row and Column Analyses . . . . . . . . . . 64
