Typical CCA Results Illustrated with an Extended Example

2 Typical CCA Results Illustrated with an Extended Example 

The numerical results of CCA are the following There are two canonical eigenvalues (roots), X1 = 0.921 and X2 = 0.851. The overall canonical correlation of X and Y (computed from the scores associated with the first eigenvalues of both sets) is 0.9596 and is highly significant. The second canonical correlation coefficient, (which may also be computed from the square root of X2) yields 0.922 and is also significant. 

The factor structure for two canonical variables (the loadings) is given in Tab. 5-8. 

These contributions represent the overall correlations with each canonical feature. Again we find factor patterns which are not very pronounced. The extraction and the redundancy measures are reported in Tab. 5-9. From the total values of the variance explained we see that both sets are well represented by their canonical variables. On the other hand the redundancy measure (90% or 72%) indicates that both feature sets may be of equal practical weight. 

By analogy with factor analysis we can now display the objects of the data set with those canonical features which extract the main portion of data variation. Fig. 5-21 shows the samples from the interlab test in the plane of the two first canonical variables. In addition to the already known special role of laboratories B and E we note some indication of the separation of the other laboratories also. 

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