Extreme Component Analysis

This module provides functionality for extreme component analysis.

An explanation and derivation of the algorithm can be found in [XCA].

[XCA]

Extreme component analysis, Welling et al (2003)

class breze.learn.xca.Xca(n_components, whiten=False)

Class implementing extreme component analysis.

The idea is that not only the prinicple components or the minor components of a data set are important, but a combination of the two. This algorithm works by combining probabilistic versions of PCA and MCA.

The central idea is that if n principle and m minor components are chosen, a gap of size D - m - n dimensions is formed in the list of singular values. The exact location of this gap is found by chosing the one which minimizes a likelihood combining PCA and MCA.

Attributes

n_components

(integer) Amount of components kept.

Methods

fit(X)	Fit the parameters of the model.
inverse_transform(F)	Perform an inverse transformation of transformed data according to the model.
reconstruct(X)	Reconstruct the data according to the model.
transform(X)	Transform data according to the model.

__init__(n_components, whiten=False)

Create an Xca object.

Parameters:

n_components : integer

Amount of components to keep.

fit(X)

Fit the parameters of the model.

The data should be centered (that is, its mean subtracted rowwise) before using this method.

Parameters:

X : array_like

An array of shape (n, d) where n is the number of data points and d the input dimensionality.

inverse_transform(F)

Perform an inverse transformation of transformed data according to the model.

Parameters:

F : array_like

An array of shape (n, d) where n is the number of data points and d the dimensionality if the feature space.

Returns:

X : array_like

An array of shape (n, c) where n is the number of samples and c is the dimensionality of the input space.

reconstruct(X)

Reconstruct the data according to the model.

Returns:

Y : array_like

An array of shape (n, d) where n is the number of samples and d is the dimensionality of the input space.

transform(X)

Transform data according to the model.

Parameters:

X : array_like

An array of shape (n, d) where n is the number of data points and d the input dimensionality.

Returns:

F : array_like

An array of shape (n, c) where n is the number of samples and c is the number of components kept.