 | PrincipalComponents Class |
Inheritance HierarchyNamespace: Novacta.Analytics
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.0.0
SyntaxThe PrincipalComponents type exposes the following members.
Properties| Name | Description | |
|---|---|---|
 | ActiveCloud |
Gets the active cloud of this instance.
(Inherited from PrincipalProjections.) |
| Contributions |
Gets the relative contributions of the projected points to the
variances of the principal variables.
(Inherited from PrincipalProjections.) |
| Coordinates |
Gets the principal coordinates of the projected points.
(Inherited from PrincipalProjections.) |
| Correlations |
Gets the correlations among the active variables and
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| Directions |
Gets the coordinates of the principal directions
w.r.t. the basis of the ActiveCloud.
(Inherited from PrincipalProjections.) |
| NumberOfDirections |
Gets the number of principal directions.
(Inherited from PrincipalProjections.) |
| RegressionCoefficients |
Gets the coefficients of the regression of each active variable on
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| RepresentationQualities |
Gets the point representation qualities on each principal direction.
(Inherited from PrincipalProjections.) |
| Variances |
Gets the variances of the principal variables.
(Inherited from PrincipalProjections.) |
Methods| Name | Description | |
|---|---|---|
  | Analyze(DoubleMatrix) |
Analyzes the principal components of the specified data.
|
| Analyze(DoubleMatrix, DoubleMatrix) |
Analyzes the principal components of data
in which individuals have received the specified weights.
|
| Analyze(DoubleMatrix, DoubleMatrix, DoubleMatrix) |
Analyzes the principal components of data
in which individuals and variables have been assigned
the specified weights and coefficients, respectively.
|
| CorrelateSupplementaryVariables(DoubleMatrix) |
Gets the correlations of each specified
supplementary variable on
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| CorrelateSupplementaryVariables(ReadOnlyDoubleMatrix) |
Gets the correlations of each specified
supplementary variable on
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) |
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) |
| GetHashCode | Serves as the default hash function. (Inherited from Object.) |
| GetType | Gets the Type of the current instance. (Inherited from Object.) |
| LocateSupplementaryPoints(DoubleMatrix) |
Gets the principal coordinates of the
specified supplementary points given
their active coordinates.
(Inherited from PrincipalProjections.) |
| LocateSupplementaryPoints(ReadOnlyDoubleMatrix) |
Gets the principal coordinates of the
specified supplementary points given
their active coordinates.
(Inherited from PrincipalProjections.) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) |
| RegressSupplementaryVariables(DoubleMatrix) |
Gets the coefficients of the regression of each specified
supplementary variable on
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| RegressSupplementaryVariables(ReadOnlyDoubleMatrix) |
Gets the coefficients of the regression of each specified
supplementary variable on
the standardized principal variables.
(Inherited from PrincipalProjections.) |
| ToString | Returns a string that represents the current object. (Inherited from Object.) |
RemarksRows of the data matrix correspond to individuals, columns to variables. Each row is interpreted as the coordinates of a multidimensional point with respect to a given basis, where the dimension is the number of possibly correlated variables observed for each individual. The analysis of the principal components aims to project the given cloud of points in a space having a reduced dimension, in which the new coordinates form uncorrelated variables which are selected by maximizing their variances, so that the projection retains as much of the variability of the initial variables as possible.
 Note |
|---|
| Components are added until the corresponding projected variance is greater than 1e-6. |
Class PrincipalComponents inherits from class PrincipalProjections. Check its documentation for a thorough explanation of the statistical methods underlying a Principal Component analysis.
Instantiation
New instances of class PrincipalComponents can be initialized by calling one of the overloaded methods Analyze(DoubleMatrix) or one of its overloaded versions. The simple overload Analyze takes a data matrix as the coordinates of the cloud with respect to the standard basis, and assigns uniform weights to each individual. Nonuniform weights can be specified through the overload Analyze, which again refers the coordinates to the standard basis.
The more complex overload Analyze takes the
coordinates matrix, the individual weights, and a sequence of
coefficients assigned to variables. Such variable coefficients
are used to refer the coordinates to a basis other than
the standard one.
More thoroughly, given the sequence of coefficients
, then
the Basis is chosen so that
its matrix is as follows:
See Also