Page 440 - Jolliffe I. Principal Component Analysis

14.7. Concluding Remarks
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space orthogonal to the components found so far. Clearly, this technique
loses the variance maximization property of PCA but, like the techniques
of Section 11.2, it can be thought of as an alternative that simplifies inter-
pretation. In the present case simplification is in the direction of the user’s
expectations.
14.7 Concluding Remarks

It has been seen in this book that PCA can be used in a wide variety of dif-
ferent ways. Many of the topics covered, especially in the last four chapters,
are of recent origin and it is likely that there will be further advances in
the near future that will help to clarify the usefulness, in practice, of some
of the newer techniques. Developments range from an increasing interest in
model-based approaches on the one hand to the mainly algorithmic ideas of
neural networks on the other. Additional uses and adaptations of PCA are
certain to be proposed and, given the large number of fields of application
in which PCA is employed, it is inevitable that there are already some uses
and modifications of which the present author is unaware.
In conclusion, it should be emphasized again that, far from being an old
and narrow technique, PCA is the subject of much recent research and has
great versatility, both in the ways in which it can be applied, and in the
fields of application for which it is useful.