.. _library_pls_projection:

pls_projection

Partial Least Squares projection reducer for target-valued continuous datasets. The library implements the dimension_reducer_protocol defined in the dimension_reduction_protocols library and learns a deterministic PLS1 projection by centering the training data, optionally standardizing continuous attributes, centering the numeric target, extracting latent directions using repeated cross-covariance maximization with sequential deflation, and storing the resulting direct projection rotations for future transforms.

Requires a dataset implementing target_supervised_dimension_reduction_dataset_protocol and therefore uses a numeric target during training.

API documentation

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

Loading

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

::

| ?- logtalk_load(pls_projection(loader)).

Testing

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

::

| ?- logtalk_load(pls_projection(tester)).

Features

• Continuous Datasets: Accepts datasets containing only continuous attributes and rejects datasets that also declare the target name as an input feature. Missing or nonnumeric values are also rejected.
• Target-Supervised Learning: Uses a numeric target attribute declared by datasets implementing target_supervised_dimension_reduction_dataset_protocol.
• Centering and Optional Scaling: Centers all attributes and optionally standardizes them before learning latent directions.
• Deterministic Components: Learns components deterministically from feature-target cross-covariance without stochastic initialization.
• Configurable Shortfall Handling: Lets callers choose whether an extraction shortfall raises an error or truncates the learned reducer with explicit diagnostics.
• Projection API: Transforms a new instance into a list of component_N-Value pairs using the learned direct PLS rotation vectors.
• 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 latent PLS components to extract. Requests that exceed min(FeatureCount, SampleCount - 1) raise domain_error(component_count, Requested-Maximum). The default is 2.
• feature_scaling/1: Whether to standardize continuous attributes before projection. Options: true (default) or false.
• shortfall_policy/1: Controls what happens when residual feature-target cross-covariance becomes negligible before all requested components are extracted. Options: truncate (default), which returns a reducer with fewer components and records a shortfall(truncated(Requested, Learned, ScoreEnergy, Tolerance)) diagnostic, or error, which raises domain_error(component_count, Requested-Learned).
• tolerance/1: Positive numerical tolerance used to stop extracting components when the residual feature-target cross-covariance becomes negligible. The default is 1.0e-8.

Usage

The following example uses the sample target-valued dataset shipped with the dimension_reduction_protocols library:

::

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

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

::

| ?- pls_projection::learn(target_latent_measurements, DimensionReducer).

| ?- pls_projection::learn(target_latent_measurements, DimensionReducer, [n_components(1), feature_scaling(false)]).

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

::

| ?- pls_projection::learn(target_latent_measurements, DimensionReducer, [n_components(2)]), pls_projection::transform(DimensionReducer, [f1-4.0, f2-8.0, f3-2.0, f4-(-2.0)], ReducedInstance).

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

::

| ?- pls_projection::learn(target_latent_measurements, DimensionReducer, [n_components(2)]), pls_projection::export_to_file(target_latent_measurements, DimensionReducer, reducer, 'pls_projection_reducer.pl').

| ?- logtalk_load('pls_projection_reducer.pl'), reducer(Reducer), pls_projection::transform(Reducer, [f1-4.0, f2-8.0, f3-2.0, f4-(-2.0)], 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:

::

pls_projection_reducer(Encoders, Rotations, Diagnostics)

Where:

• Encoders: List of continuous attribute encoders storing attribute name, mean, and scale.
• Rotations: List of direct PLS projection vectors derived from the learned latent weights and loadings.
• Diagnostics: Learned metadata including the effective training options, target information, target loadings, and optional truncate-mode shortfall 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. Wold, H. (1975) - "Soft modelling by latent variables; the nonlinear iterative partial least squares (NIPALS) approach".
2. Geladi, P. and Kowalski, B. R. (1986) - "Partial least-squares regression: a tutorial".