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SPDX-FileCopyrightText: 1998-2026 Paulo Moura <pmoura@logtalk.org>
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`pca_projection`
=====

Principal Component Analysis reducer for continuous datasets. The
library implements the `dimension_reducer_protocol` defined in the
`dimension_reduction_protocols` library and learns a linear projection
by centering the training data, optionally standardizing continuous
attributes, computing the covariance matrix, and extracting principal
components using deterministic power iteration with deflation.


API documentation
-----------------

Open the [../../apis/library_index.html#pca_projection](../../apis/library_index.html#pca_projection)
link in a web browser.


Loading
-------

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

	| ?- logtalk_load(pca_projection(loader)).


Testing
-------

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

	| ?- logtalk_load(pca_projection(tester)).


Features
--------

- **Continuous Datasets**: Accepts datasets containing only continuous attributes.
- **Centering and Optional Scaling**: Centers all attributes and optionally standardizes them before extracting principal directions.
- **Portable Eigensolver**: Uses deterministic power iteration with deflation instead of backend-specific linear algebra libraries.
- **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.
- **Missing Values**: Missing or nonnumeric values are rejected.


Options
-------

The `learn/3` predicate accepts the following options:

- `n_components/1`: Number of principal components to extract. Requests that exceed the number of features raise `domain_error(component_count, Requested-Maximum)`. The default is `2`.
- `feature_scaling/1`: Whether to standardize continuous attributes before extracting components. Options: `true` (default) or `false`.
- `maximum_iterations/1`: Maximum number of power-iteration steps used when estimating each principal direction. The default is `1000`.
- `tolerance/1`: Positive convergence tolerance used both for power-iteration stopping and for deciding when deflated eigenvalues are negligible. The default is `1.0e-8`.


Usage
-----

The following examples use the sample datasets shipped with the
`dimension_reduction_protocols` library:

	| ?- logtalk_load(dimension_reduction_protocols('test_datasets/correlated_plane')),
	     logtalk_load(dimension_reduction_protocols('test_datasets/high_dimensional_measurements')).

### Learning a reducer

	| ?- pca_projection::learn(correlated_plane, DimensionReducer).

	| ?- pca_projection::learn(correlated_plane, DimensionReducer, [n_components(1), feature_scaling(false), maximum_iterations(200), tolerance(1.0e-7)]).

### Transforming new instances

	| ?- pca_projection::learn(high_dimensional_measurements, DimensionReducer),
	     pca_projection::transform(DimensionReducer, [f1-0.9, f2-1.1, f3-1.0, f4-2.0, f5-2.2, f6-2.1], ReducedInstance).

	| ?- pca_projection::learn(correlated_plane, DimensionReducer, [n_components(1)]),
	     pca_projection::transform(DimensionReducer, [x-1.0, y-2.0, z-3.0], ReducedInstance).

### Exporting and reusing the reducer

	| ?- pca_projection::learn(correlated_plane, DimensionReducer, [n_components(1)]),
	     pca_projection::export_to_file(correlated_plane, DimensionReducer, reducer, 'pca_reducer.pl').

	| ?- logtalk_load('pca_reducer.pl'),
	     reducer(Reducer),
	     pca_projection::transform(Reducer, [x-1.0, y-2.0, z-3.0], ReducedInstance).


Dimension reducer representation
-------------------------------

The learned dimension reducer is represented by a compound term with the
functor chosen by the implementation and arity 4. For example:

	pca_reducer(Encoders, Components, ExplainedVariances, Diagnostics)

Where:

- `Encoders`: List of continuous attribute encoders storing attribute name, mean, and scale.
- `Components`: List of principal direction vectors in descending variance order.
- `ExplainedVariances`: List of eigenvalues matching the extracted components.
- `Diagnostics`: Learned reducer metadata including the effective training options and learned model details.

When exported using `export_to_clauses/4` or
`export_to_file/4`, this reducer term is serialized directly
as the single argument of the generated predicate clause so that the
exported model can be loaded and reused as-is.


References
----------

1. Pearson, K. (1901) - "On lines and planes of closest fit to systems of points in space".
2. Hotelling, H. (1933) - "Analysis of a complex of statistical variables into principal components".
