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java.lang.Object com.numericalmethod.suanshu.stats.pca.PCAbySVD
public class PCAbySVD
This class performs Principal Component Analysis (PCA) on a data matrix, using the preferred Singular Value Decomposition (SVD) method.
PCA essentially rotates the set of points around their mean in order to align with the principal components. This moves as much of the variance as possible (using an orthogonal transformation) into the first few dimensions. The values in the remaining dimensions, therefore, tend to be small and may be dropped with minimal loss of information.
The R equivalent function is prcomp
.
Constructor Summary  

PCAbySVD(Matrix data)
Performs Principal Component Analysis, using the preferred SVD method, on a centered and scaled data matrix. 

PCAbySVD(Matrix data,
boolean centered,
boolean scaled)
Performs Principal Component Analysis, using the preferred SVD method, on a data matrix (possibly centered and/or scaled). 

PCAbySVD(Matrix data,
Vector mean,
Vector scale)
Performs Principal Component Analysis, using the preferred SVD method, on a data matrix with (optional) mean vector and scaling vector provided. 
Method Summary  

DenseVector 
cumulativeProportionVar()
Gets the cumulative proportion of overall variance explained by the principal components 
ImmutableMatrix 
data()
Gets the original data matrix. 
Vector 
loading(int i)
Gets the loading vector of the ith principal component. 
Matrix 
loadings()
Gets the matrix of variable loadings. 
Vector 
mean()
Gets the sample means that were subtracted. 
int 
nFactors()
Gets the number of variables in the original data. 
int 
nObs()
Gets the number of observations in the original data; sample size. 
Vector 
proportionVar()
Gets the proportion of overall variance explained by each of the principal components. 
double 
proportionVar(int i)
Gets the proportion of overall variance explained by the ith principal component. 
Vector 
scale()
Gets the scalings applied to each variable. 
Matrix 
scores()
Gets the scores of supplied data on the principal components. 
double 
sdPrincipalComponent(int i)
Gets the standard deviation of the ith principal component. 
DenseVector 
sdPrincipalComponents()
Gets the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the correlation (or covariance) matrix, though the calculation is actually done with the singular values of the data matrix) 
SVD 
svd()
Gets the Singular Value Decomposition (SVD) of matrix X. 
Matrix 
X()
Gets the (possibly centered and/or scaled) data matrix X used for the PCA. 
Methods inherited from class java.lang.Object 

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 

public PCAbySVD(Matrix data, Vector mean, Vector scale)
data
 a matrix that represents the original datamean
 an optional mean vector (of length equal to nFactors) to be subtracted
regardless of the flag centered
scale
 an optional scaling vector (of length equal to nFactors) to be divided
regardless of the flag scaled
public PCAbySVD(Matrix data, boolean centered, boolean scaled)
data
 a matrix that represents the original datacentered
 a logical value indicating whether the variables should be shifted to be zero
centeredscaled
 a logical value indicating whether the variables should be scaled to have
unit variance before the analysis takes place
(N.B. in general scaling is advisable; however, it should only be used if there is no
constant variable)public PCAbySVD(Matrix data)
data
 a matrix that represents the original dataMethod Detail 

public Vector mean()
PCA
mean
in interface PCA
public Vector scale()
PCA
scale
in interface PCA
public SVD svd()
public DenseVector sdPrincipalComponents()
public Matrix loadings()
PCA
public ImmutableMatrix data()
public int nObs()
PCA
nObs
in interface PCA
public int nFactors()
PCA
nFactors
in interface PCA
public Matrix X()
PCA
X
in interface PCA
public double sdPrincipalComponent(int i)
PCA
sdPrincipalComponent
in interface PCA
i
 an index, counting from 1
public Vector loading(int i)
PCA
loading
in interface PCA
i
 an index, counting from 1
public Vector proportionVar()
PCA
proportionVar
in interface PCA
public double proportionVar(int i)
PCA
proportionVar
in interface PCA
i
 an index, counting from 1
public DenseVector cumulativeProportionVar()
PCA
cumulativeProportionVar
in interface PCA
public Matrix scores()
PCA
scores
in interface PCA


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