## Posts Tagged ‘PCA’

### Formulating the PCA

Today I have thought about how one can formulate the Principal Component Analysis (PCA) method. In particular I want to reformulate PCA as a solution for a regression problem. The idea of reformulation PCA as a solution for some regression problem is useful in Sparse PCA , in which a $L_1$ regularization term is inserted into a ridge regression formula to enforce spareness of the coefficients (i.e. elastic net). There are at least two equivalent ways to motivate PCA. In this post I will first give a formulation of PCA based on orthogonal projection, and then discuss a regression-type reformulation of PCA.