Extracting information from good data

Principal components analysis

• Maximize variance in a minimum number of dimensions.

• Graphically, twist the original data axes to conform with the axes containing the most variance information.

As much variance is possible is rotated into X'.

The rest is rotated into Y'.

• Mathematically, a simple linear algebra transform of the data.

• Factor analysis can be used to modify the results of PCS, seeking more interpretable factors.

• PCA and factor analysis reduce the number of variables, yielding a new set which often describe important, but unmeasurable properties.

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