Principal Component Analysis (PCA)

As a data processing method, Principal Component Analysis (PCA) is often used to reduce the dimensionality of a dataset. But PCA is not a panacea for all cases, it works when some dimensions of the dataset is highly linear related. For example, in the driving domain, the driver's gas/brake action is decided by the curvature of the road, the vehicle's speed and yaw, the traffic condition, etc. and some of their previous values and/or the values in the future. Hence, the dimensionality of the input can be very large, say 56. However, many dimensions of the input are intensively linear related, so that the dimensionality of the input can be greatly reduced to something like 3, without great loss of any information.

• The core technique of PCA is Singular Value Decomposition (SVD), referring to W.H.Press et al., Numerical Recipes in C, the Art of Scientific Computing , 1994 pp 59 to 70.
• C.M.Bishop's Neural Network for Pattern Recognition , 1995, pp 310 to 313, gives a brief introduction to the basic idea of PCA.
• I.T.Jolliffe's Principal Component Analysis , Springer Series in Statistics 1986, discusses PCA in every detail in the point of view of statisticians.