Romeil Sandhu
Lecture Notes [retrieved from], 2014
Publication year: 2014

PCA has provided the quantitive finance community a manner for factor analysis, dimensional reduction, and prediction. However, two main drawbacks of this approach is in the construction: (1) PCA assumes a Gaussian distribution capturing outliers. (2) There is a linearity assumption that often violated in PCA. While there are numerous methods to counter PCA (e.g., attaching differing underlying distributions such as the Student T), it remains powerful do ease of use.  Over several discussions, I decided to put together a set of notes if one were to extend PCA to the nonlinear case to illustrate the complexity (and advantages).  These notes herein are simply a tutorial for those interested.