PrincipalComponentAnalysis Class 
Namespace: Meta.Numerics.Statistics
The PrincipalComponentAnalysis type exposes the following members.
Name  Description  

Component 
Gets the requested principal component.
 
Equals  (Inherited from Object.)  
GetHashCode  Serves as a hash function for a particular type. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
MinimumDimension 
Gets the minimum number of principal components that must be included to explain the given fraction of the total variance.
 
ToString  Returns a string that represents the current object. (Inherited from Object.)  
TransformedSample 
Represents the original data in terms of principal components.

Principal component analysis (PCA) is a form of factor analysis. It attempts to identify a small number number of factors such that, by specifing only values of these few factors for each row, the value of each variable can be accurately predicted.
Mathematically, PCA constructs an alternative set of orthonormal basis vectors for a multivariate data set. These basis vectors, called principal components, are ordered by the total variance explained by each.
Suppose, for example, you measure the value of different possessions possessions for a sample of people: home value, car value, furniture value, etc. You might expect that much of the variation in these numbers can be explained by one underlying factor, which you might call "richness". If this is true, then a PCA analysis will show that the most principal component explains a very large faction of the total variance, and the other less principal components will explain only small fractions of the total variance.
Note that PCA is not invariant with respect to the rescaling of individual variables.
Note that PCA is an exploratory technique, not a hypothesis test.