Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)
Syntax
| C# | Visual Basic | Visual C++ | F# |
public sealed class PrincipalComponentAnalysis
Public NotInheritable Class PrincipalComponentAnalysis
public ref class PrincipalComponentAnalysis sealed
[<SealedAttribute>] type PrincipalComponentAnalysis = class end
Members
| All Members | Properties  | Methods  |
 Public Protected | Instance Static  | Declared Inherited | XNA Framework Only  .NET Compact Framework Only  |
| Member | Description | |
|---|---|---|
| Component(Int32) |
Gets the requested principal component.
|
| Count |
Gets the number of data entries.
|
| Dimension |
Gets the number of components.
|
| Equals(Object) | (Inherited from Object.) |
 | Finalize()()()() | Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection. (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.) |
| MemberwiseClone()()()() | Creates a shallow copy of the current Object. (Inherited from Object.) |
| MinimumDimension(Double) |
Gets the minimum number of principal components that must be included to explain the given fraction of the total variance.
|
| ToString()()()() | (Inherited from Object.) |
| TransformedSample()()()() |
Represents the original data in terms of principal components.
|
Remarks
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 multi-variate 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 re-scaling of individual variables.
Note that PCA is an exploratory technique, not a hypothesis test.
