ica_projection — Logtalk 3.100.1

# `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 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

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