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PrincipalComponentAnalysis Class
Represents a principal component analysis.
Inheritance Hierarchy
SystemObject
  Meta.Numerics.StatisticsPrincipalComponentAnalysis

Namespace:  Meta.Numerics.Statistics
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public sealed class PrincipalComponentAnalysis

The PrincipalComponentAnalysis type exposes the following members.

Properties
  NameDescription
Public propertyCount
Gets the number of data entries.
Public propertyDimension
Gets the number of components.
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Methods
  NameDescription
Public methodComponent
Gets the requested principal component.
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodMinimumDimension
Gets the minimum number of principal components that must be included to explain the given fraction of the total variance.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Public methodTransformedSample
Represents the original data in terms of principal components.
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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.

See Also