Class PCA
 All Implemented Interfaces:
Serializable
,Function<Tuple,
,Tuple> Transform
PCA is mostly used as a tool in exploratory data analysis and for making predictive models. PCA involves the calculation of the eigenvalue decomposition of a data covariance matrix or singular value decomposition of a data matrix, usually after mean centering the data for each attribute. The results of a PCA are usually discussed in terms of component scores and loadings.
As a linear technique, PCA is built for several purposes: first, it enables us to decorrelate the original variables; second, to carry out data compression, where we pay decreasing attention to the numerical accuracy by which we encode the sequence of principal components; third, to reconstruct the original input data using a reduced number of variables according to a leastsquares criterion; and fourth, to identify potential clusters in the data.
In certain applications, PCA can be misleading. PCA is heavily influenced when there are outliers in the data. In other situations, the linearity of PCA may be an obstacle to successful data reduction and compression.
 See Also:

Field Summary
Fields inherited from class smile.feature.extraction.Projection
columns, projection, schema

Constructor Summary

Method Summary
Modifier and TypeMethodDescriptiondouble[]
center()
Returns the center of data.static PCA
Fits principal component analysis with correlation matrix.static PCA
Fits principal component analysis with correlation matrix.double[]
Returns the cumulative proportion of variance contained in principal components, ordered from largest to smallest.static PCA
Fits principal component analysis with covariance matrix.static PCA
Fits principal component analysis with covariance matrix.getProjection
(double p) Returns the projection with top principal components that contain (more than) the given percentage of variance.getProjection
(int p) Returns the projection with given number of principal components.loadings()
Returns the variable loading matrix, ordered from largest to smallest by corresponding eigenvalues.protected double[]
postprocess
(double[] x) Postprocess the output vector after projection.double[]
variance()
Returns the principal component variances, ordered from largest to smallest, which are the eigenvalues of the covariance or correlation matrix of learning data.double[]
Returns the proportion of variance contained in each principal component, ordered from largest to smallest.Methods inherited from class smile.feature.extraction.Projection
apply, apply, apply, apply, preprocess

Constructor Details

PCA
Constructor. Parameters:
mu
 the mean of samples.eigvalues
 the eigen values of principal components.loadings
 the matrix of variable loadings.projection
 the projection matrix.columns
 the columns to transform when applied on Tuple/DataFrame.


Method Details

fit
Fits principal component analysis with covariance matrix. Parameters:
data
 training data of which each row is a sample.columns
 the columns to fit PCA. If empty, all columns will be used. Returns:
 the model.

cor
Fits principal component analysis with correlation matrix. Parameters:
data
 training data of which each row is a sample.columns
 the columns to fit PCA. If empty, all columns will be used. Returns:
 the model.

fit
Fits principal component analysis with covariance matrix. Parameters:
data
 training data of which each row is a sample.columns
 the columns to transform when applied on Tuple/DataFrame. Returns:
 the model.

cor
Fits principal component analysis with correlation matrix. Parameters:
data
 training data of which each row is a sample.columns
 the columns to transform when applied on Tuple/DataFrame. Returns:
 the model.

center
public double[] center()Returns the center of data. Returns:
 the center of data.

loadings
Returns the variable loading matrix, ordered from largest to smallest by corresponding eigenvalues. The matrix columns contain the eigenvectors. Returns:
 the variable loading matrix.

variance
public double[] variance()Returns the principal component variances, ordered from largest to smallest, which are the eigenvalues of the covariance or correlation matrix of learning data. Returns:
 the principal component variances.

varianceProportion
public double[] varianceProportion()Returns the proportion of variance contained in each principal component, ordered from largest to smallest. Returns:
 the proportion of variance contained in each principal component.

cumulativeVarianceProportion
public double[] cumulativeVarianceProportion()Returns the cumulative proportion of variance contained in principal components, ordered from largest to smallest. Returns:
 the cumulative proportion of variance.

getProjection
Returns the projection with given number of principal components. Parameters:
p
 choose top p principal components used for projection. Returns:
 a new PCA projection.

getProjection
Returns the projection with top principal components that contain (more than) the given percentage of variance. Parameters:
p
 the required percentage of variance. Returns:
 a new PCA projection.

postprocess
protected double[] postprocess(double[] x) Description copied from class:Projection
Postprocess the output vector after projection. Overrides:
postprocess
in classProjection
 Parameters:
x
 the output vector of projection. Returns:
 the postprocessed vector.
