smile.projection

Class PPCA

java.lang.Object

smile.projection.PPCA

All Implemented Interfaces:

java.io.Serializable, LinearProjection, Projection<double[]>

public class PPCA
extends java.lang.Object
implements LinearProjection, java.io.Serializable

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 (Ψ_i = 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

Constructor Summary

Constructors

Constructor and Description
PPCA(double noise, double[] mu, smile.math.matrix.DenseMatrix loading, smile.math.matrix.DenseMatrix projection) Constructor.

Method Summary

Modifier and Type	Method and Description
static PPCA	fit(double[][] data, int k) Fits probabilistic principal component analysis.
double[]	getCenter() Returns the center of data.
smile.math.matrix.DenseMatrix	getLoadings() Returns the variable loading matrix, ordered from largest to smallest by corresponding eigenvalues.
double	getNoiseVariance() Returns the variance of noise.
smile.math.matrix.DenseMatrix	getProjection() Returns the projection matrix.
double[]	project(double[] x) Project a data point to the feature space.
double[][]	project(double[][] x) Project a set of data to the feature space.

Methods inherited from class java.lang.Object

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

Constructor Detail

PPCA

public PPCA(double noise,
            double[] mu,
            smile.math.matrix.DenseMatrix loading,
            smile.math.matrix.DenseMatrix projection)

Constructor.

Parameters:

noise - the variance of noise.

mu - the mean of samples.

loading - the loading matrix.

projection - the projection matrix.

Method Detail

getLoadings

public smile.math.matrix.DenseMatrix getLoadings()

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

getCenter

public double[] getCenter()

Returns the center of data.

getNoiseVariance

public double getNoiseVariance()

Returns the variance of noise.

getProjection

public smile.math.matrix.DenseMatrix getProjection()

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

Specified by:

getProjection in interface LinearProjection

project

public double[] project(double[] x)

Description copied from interface: Projection

Project a data point to the feature space.

Specified by:

project in interface LinearProjection

Specified by:

project in interface Projection<double[]>

project

public double[][] project(double[][] x)

Description copied from interface: Projection

Project a set of data to the feature space.

Specified by:

project in interface LinearProjection

Specified by:

project in interface Projection<double[]>

fit

public static PPCA fit(double[][] data,
                       int k)

Fits probabilistic principal component analysis.

Parameters:

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

k - the number of principal component to learn.