Background of PCA

PCA is based on an orthogonal, linear transformation of data into a new representation space. It can be thought of as a replacement of the original attributes by new attributes, so-called principal components. These principal components correspond to the directions in the original attribute space that shows the greatest variance.

The number of principal components that are used is at most identical to the number of original attributes. Often, however, the number is considerably lower, because one goal of PCA is the reduction of dimensionality. Whereas simple algorithms for data exploration might be sufficient for exploring single attributes or pairs of attributes, PCA is most useful for multidimensional data that has several attributes. For multidimensional data, simple algorithms are not sufficient.

If the analyzed data set shows strong patterns, the dimension of the new representation that is obtained by using PCA can be considerably reduced without significant loss of information.