Questions about the application of PCA I'm learning about PCA. In general, I understand the concept and the underlying math, but I'm confused about a few things that I'm hoping someone can explain. 
Lets say that after performing a PCA analysis on some high dimensional data I find that the first three components capture 99% of the variance in my data. Now what? Is it possible to find which features comprise the first, second, and third components? It seems that a common approach is to plot the principle components. For example, see this page under 2.3.1. Dimensionality Reduction and visualization for a PCA plot of the iris data. What is the interpretation of this plot? I see what I presume are two components: one component in red one component a mixture of green and blue? 
Is there a general "next step" to do after PCA. I understand the concept, but fail to see how it can be practically applied. Thanks for the help. 
 A: First, the interpretation of the plot from the page you linked to. Each point is a data point from iris data set, transformed by PCA to 2-dimensional representation. The colors refer to distinct classes of irises (setosa, versicolor, virginica), not to principal components.
As Michael said, each principal component is a linear function of the variables. To see the coefficients of this function you can check the coefficients_ attribute in the PCA object from the tutorial you linked to.
The general next step after getting the components (each one a different linear function) is to apply those functions to the data, and get new lower-dimensional representation of the data. If the data was 100-dimensional, and you chose 7 principal components which explain a satisfactory portion of variance, you can from now on work on 7-dimensional data instead, which is easier and faster.
If you want to see a mathematical proof of PCA which uses only linear algebra, and which I hope will give you a good understanding of what PCA does, and how it does it, I have written one lately here : Making sense of principal component analysis, eigenvectors & eigenvalues
A: Well yes.  Look a the magnitude of the coefficients in the linear combination of the components.  That tells you how each variable contributes to each of these first few principal components.
