Monday, April 26, 2010

Linear discriminant analysis on PCA factors

In this tutorial, we show that in certain circumstances, it is more convenient to use the factors computed from a principal component analysis (from the original attributes) as input features for the linear discriminant analysis algorithm.

The new representation space maintains the proximity between the examples. The new features known as "factors" or "latent variables", which are a linear combination of the original descriptors, have several advantageous properties: (a) their interpretation very often allows to detect patterns in the initial space; (b) a very reduced number of factors allows to restore information contained in the data, we can moreover remove the noise from the dataset by using only the most relevant factors (it is a sort of regularization by smoothing the information provided by the dataset); (c) the new features form an orthogonal basis, learning algorithms such as linear discriminant analysis have a better behavior.

This approach has a connection to the reduced-rank linear discriminant analysis. But, instead to this last one, the class information is not needed during the computations of the principal components. The computation can be very fast using an appropriate algorithm when we deal with very high-dimensional dataset (such as NIPALS). But, on the other hand, it seems that the standard reduced-rank LDA tends to be better in terms of classification accuracy.

Keywords: linear discriminant analysis, principal component analysis, reduced-rank linear discriminant analysis
Components: Supervised Learning, Linear discriminant analysis, Principal Component Analysis, Scatterplot, Train-test
Tutorial: en_dr_utiliser_axes_factoriels_descripteurs.pdf
Dataset: dr_waveform.bdm
Wikipedia, "Linear discriminant analysis".