Class ProbabilisticPCA

java.lang.Object

smile.feature.extraction.Projection

smile.feature.extraction.ProbabilisticPCA

All Implemented Interfaces:

Serializable, Function<Tuple,Tuple>, Transform

public class ProbabilisticPCA
extends Projection

Probabilistic principal component analysis. Probabilistic PCA is a simplified factor analysis that employs a latent variable model with linear relationship:

    y ∼ W * x + μ + ε

where latent variables x ∼ N(0, I), error (or noise) ε ∼ N(0, Ψ), and μ is the location term (mean). In probabilistic PCA, an isotropic noise model is used, i.e., noise variances constrained to be equal (Ψi = σ2). A close form of estimation of above parameters can be obtained by maximum likelihood method.

References

1. Michael E. Tipping and Christopher M. Bishop. Probabilistic Principal Component Analysis. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 61(3):611-622, 1999.

See Also:

• PCA
• Serialized Form

Field Summary

Fields inherited from class Projection

columns, projection, schema

Constructor Summary

Constructors

Constructor	Description
ProbabilisticPCA(double noise, double[] mu, DenseMatrix loading, DenseMatrix projection, String... columns)	Constructor.

Method Summary

Modifier and Type	Method	Description
Vector	center()	Returns the center of data.
static ProbabilisticPCA	fit(double[][] data, int k, String... columns)	Fits probabilistic principal component analysis.
static ProbabilisticPCA	fit(DataFrame data, int k, String... columns)	Fits probabilistic principal component analysis.
DenseMatrix	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 variance of noise.

Methods inherited from class Projection

apply, apply, apply, apply, preprocess

Methods inherited from class Object

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

Methods inherited from interface Function

andThen, compose

Methods inherited from interface Transform

andThen, compose

Constructor Details

ProbabilisticPCA

public ProbabilisticPCA(double noise,
 double[] mu,
 DenseMatrix loading,
 DenseMatrix projection,
 String... columns)

Constructor.

Parameters:

noise - the variance of noise.

mu - the mean of samples.

loading - the loading matrix.

projection - the projection matrix. Note that this is not the matrix W in the latent model.

columns - the columns to transform when applied on Tuple/DataFrame.

Method Details

loadings

public DenseMatrix loadings()

Returns the variable loading matrix, ordered from largest to smallest by corresponding eigenvalues.

Returns:

the variable loading matrix.

center

public Vector center()

Returns the center of data.

Returns:

the center of data.

variance

public double variance()

Returns the variance of noise.

Returns:

the variance of noise.

postprocess

protected double[] postprocess(double[] x)

Description copied from class: Projection

Postprocess the output vector after projection.

Overrides:

postprocess in class Projection

Parameters:

x - the output vector of projection.

Returns:

the postprocessed vector.

fit

public static ProbabilisticPCA fit(DataFrame data,
 int k,
 String... columns)

Fits probabilistic principal component analysis.

Parameters:

data - training data of which each row is a sample.

k - the number of principal component to learn.

columns - the columns to fit PCA. If empty, all columns will be used.

Returns:

the model.

fit

public static ProbabilisticPCA fit(double[][] data,
 int k,
 String... columns)

Fits probabilistic principal component analysis.

Parameters:

data - training data of which each row is a sample.

k - the number of principal component to learn.

columns - the columns to transform when applied on Tuple/DataFrame.

Returns:

the model.