.. _library_truncated_svd_projection:

`truncated_svd_projection`

Truncated singular value decomposition reducer for continuous datasets. The library implements the dimension_reducer_protocol defined in the dimension_reduction_protocols library and learns a low-rank linear projection by building a preprocessed data matrix using optional centering and scaling, extracting singular triplets using deterministic two-sided power iteration, and applying rank-one deflation directly to the data matrix.

API documentation

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

Loading

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

| ?- logtalk_load(truncated_svd_projection(loader)).

Testing

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

| ?- logtalk_load(truncated_svd_projection(tester)).

Features

Continuous Datasets: Accepts datasets containing only continuous attributes. Missing or nonnumeric values are rejected.
Low-Rank Projection: Extracts right singular vectors and singular values in descending order.
Portable SVD Solver: Uses deterministic two-sided power iteration with rank-one deflation over the data matrix instead of backend-specific linear algebra libraries.
Optional Centering and Scaling: Supports explicit control over whether training and transform inputs are centered and/or scaled.
Training Diagnostics: Records per-component convergence reasons, iteration counts, and final deltas alongside the learned singular values.
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 singular vectors to extract. The default is 2. Requests that exceed the numerical rank after shape capping raise domain_error(component_count, Requested-Extracted) instead of silently returning fewer components.
center/1: Whether to center the training and transform inputs using the training-set means. Options: true or false (default).
feature_scaling/1: Whether to divide each continuous attribute by its training-set standard deviation. Options: true or false (default).
maximum_iterations/1: Maximum number of power-iteration steps used when estimating each singular vector. The default is 1000.
tolerance/1: Positive convergence tolerance used both for power-iteration stopping and for deciding when the residual matrix no longer supports the requested number of components. The default is 1.0e-8.
The learned diagnostics also include:
convergence(Statuses): Per-component stop reasons, such as tolerance or maximum_iterations_exhausted.
iterations(Counts): Per-component iteration counts aligned with the extracted singular vectors.
final_delta(Deltas): Per-component final update magnitudes aligned with the extracted singular vectors.

Usage

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

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

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

| ?- truncated_svd_projection::learn(low_rank_rectangular, DimensionReducer).

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

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

| ?- truncated_svd_projection::learn(low_rank_rectangular, DimensionReducer), truncated_svd_projection::transform(DimensionReducer, [f1-1.0, f2-1.0, f3-2.0], ReducedInstance).

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

| ?- truncated_svd_projection::learn(low_rank_rectangular, DimensionReducer, [n_components(1)]), truncated_svd_projection::export_to_file(low_rank_rectangular, DimensionReducer, reducer, 'truncated_svd_reducer.pl').

| ?- logtalk_load('truncated_svd_reducer.pl'), reducer(Reducer), truncated_svd_projection::transform(Reducer, [f1-1.0, f2-1.0, f3-2.0], ReducedInstance).

Dimension reducer representation

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

truncated_svd_reducer(Encoders, Components, SingularValues, Diagnostics)

Where:

Encoders: List of continuous attribute encoders storing attribute name, centering offset, and scale factor.
Components: List of right singular vectors in descending singular-value order.
SingularValues: List of singular values matching the extracted components.
Diagnostics: Learned reducer metadata including the effective training options, singular values, and per-component convergence information.

References

Eckart, C. and Young, G. (1936) - "The approximation of one matrix by another of lower rank".