.. _library_ica_projection:

`ica_projection`

Independent Component Analysis reducer for continuous datasets (missing or non-numeric values are rejected). The library implements the dimension_reducer_protocol defined in the dimension_reduction_protocols library and learns a linear unmixing projection by centering the training data, optionally standardizing continuous attributes, whitening the covariance matrix using the shared deterministic symmetric eigen-decomposition from linear_algebra, and then extracting independent components using a deterministic cubic FastICA fixed-point iteration with orthogonal deflation.

API documentation

Open the `../../apis/library_index.html#ica_projection <../../apis/library_index.html#ica_projection>`__ link in a web browser.

Loading

To load this library, load the loader.lgt file:

| ?- logtalk_load(ica_projection(loader)).

Testing

To test this library predicates, load the tester.lgt file:

| ?- logtalk_load(ica_projection(tester)).

Features

Continuous Datasets: Accepts datasets containing only continuous attributes.
Shared Symmetric Whitening Plus Fixed-Point ICA: Whitens the training covariance matrix using the shared symmetric eigendecomposition from linear_algebra and then extracts independent directions using deterministic cubic FastICA with orthogonal deflation.
Always Centered: Training and transform inputs are always centered using the training-set means before whitening and projection.
Optional Scaling: Can optionally standardize each continuous attribute before whitening.
Training Diagnostics: Records whitening eigenvalues plus per-component convergence reasons, iteration counts, and final deltas.
Projection API: Transforms a new instance into a list of component_N-Value pairs.
Model Export: Learned reducers can be exported as predicate clauses or written to a file.

Options

The learn/3 predicate accepts the following options:

n_components/1: Number of independent components to extract. Because training data is always centered, requests that exceed min(feature_count, sample_count - 1) raise domain_error(component_count, Requested-Maximum). Requests that still exceed the numerical rank of the whitened covariance matrix raise domain_error(component_count, Requested-Extracted). The default is 2.
feature_scaling/1: Whether to divide each continuous attribute by its training-set standard deviation before whitening. Options: true or false (default).
maximum_iterations/1: Maximum iteration bound used both by the whitening eigensolver and by the FastICA fixed-point steps for each independent component. The default is 1000.
tolerance/1: Positive convergence tolerance used both for whitening rank detection and for FastICA fixed-point stopping. The default is 1.0e-8.
The learned diagnostics also include:
whitening_eigenvalues(Values): Eigenvalues used to build the whitening transform, aligned with the extracted components.
convergence(Statuses): Per-component stop reasons, such as tolerance or maximum_iterations_exhausted.
iterations(Counts): Per-component iteration counts aligned with the extracted components.
final_delta(Deltas): Per-component final update magnitudes aligned with the extracted components.

Usage

The following examples use the sample dataset shipped with the dimension_reduction_protocols library:

| ?- logtalk_load(dimension_reduction_protocols('test_datasets/mixed_independent_sources')).

Learning a reducer ~~~~~~~~~~~~~~~~~~

| ?- ica_projection::learn(mixed_independent_sources, DimensionReducer).

| ?- ica_projection::learn(mixed_independent_sources, DimensionReducer, [n_components(2), feature_scaling(true), maximum_iterations(200), tolerance(1.0e-7)]).

Transforming new instances ~~~~~~~~~~~~~~~~~~~~~~~~~~

| ?- ica_projection::learn(mixed_independent_sources, DimensionReducer), ica_projection::transform(DimensionReducer, [x1-(-5.0), x2-(-4.0), x3-(-4.0)], ReducedInstance).

Exporting and reusing the reducer ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

| ?- ica_projection::learn(mixed_independent_sources, DimensionReducer, [n_components(2)]), ica_projection::export_to_file(mixed_independent_sources, DimensionReducer, reducer, 'ica_reducer.pl').

| ?- logtalk_load('ica_reducer.pl'), reducer(Reducer), ica_projection::transform(Reducer, [x1-(-5.0), x2-(-4.0), x3-(-4.0)], ReducedInstance).

Dimension reducer representation

The learned dimension reducer is represented by a compound term with the functor chosen by the implementation and arity 3. For example:

ica_reducer(Encoders, Components, Diagnostics)

Where:

Encoders: List of continuous attribute encoders storing attribute name, centering offset, and scale factor.
Components: List of learned unmixing vectors in feature space.
Diagnostics: Learned reducer metadata including the effective training options, whitening eigenvalues, and per-component convergence information.

References

Hyvarinen, A. and Oja, E. (2000) - "Independent Component Analysis: Algorithms and Applications".