A Tutorial on Principal Components Analysis by Lindsay I. Smith.
From Chapter 3:
Finally we come to Principal Components Analysis (PCA). What is it? It is a way of identifying patterns in data, and expressing the data in such a way as to highlight their similarities and differences. Since patterns in data can be hard to find in data of high dimension, where the luxury of graphical representation is not available, PCA is a powerful tool for analysing data.
The other main advantage of PCA is that once you have found these patterns in the data, and you compress the data, ie. by reducing the number of dimensions, without much loss of information. This technique used in image compression, as we will see in a later section.
One of the main application areas for PCA is image analysis, recognition.
Lindsay starts off with a review of the mathematics needed to work through the rest of the material.
Topic maps are a natural fit for pairing up the results of image recognition, for example, and other data. More on that anon.