`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 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

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

pca_projection