random_projection — Logtalk 3.100.1

# `random_projection`

Random projection reducer for continuous datasets. The library implements the `dimension_reducer_protocol` defined in the `dimension_reduction_protocols` library and learns a seeded dense Rademacher projection matrix using the portable `fast_random` pseudo-random generator after centering the training data, optionally standardizing continuous attributes, and sampling entries in `{-$1/sqrt(k)$, +$1/sqrt(k)$}` where `$k$` is the requested reduced dimensionality.

## API documentation

Open the ../../apis/library_index.html#random_projection link in a web browser.

## Loading

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

    | ?- logtalk_load(random_projection(loader)).

## Testing

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

    | ?- logtalk_load(random_projection(tester)).

## Features

- Continuous Datasets: Accepts datasets containing only continuous attributes. Missing or nonnumeric values are rejected.

- Centering and Optional Scaling: Centers all attributes and optionally standardizes them before projection.

- Portable Seeded Sampling: Uses `fast_random(xoshiro128pp)` so learned projection matrices are portable and reproducible.

- 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 random projection components to sample. 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 projection. Options: `true` (default) or `false`.

- `random_seed/1`: Positive integer used to seed the portable pseudo-random generator before sampling the projection matrix. The default is `1357911`.

## 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

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

    | ?- random_projection::learn(correlated_plane, DimensionReducer, [n_components(1), feature_scaling(false), random_seed(17)]).

### Transforming new instances

    | ?- random_projection::learn(high_dimensional_measurements, DimensionReducer, [random_seed(11)]),
         random_projection::transform(DimensionReducer, [f1-0.9, f2-1.1, f3-1.0, f4-2.0, f5-2.2, f6-2.1], ReducedInstance).

    | ?- random_projection::learn(correlated_plane, DimensionReducer, [n_components(1), random_seed(19)]),
         random_projection::transform(DimensionReducer, [x-1.0, y-2.0, z-3.0], ReducedInstance).

### Exporting and reusing the reducer

    | ?- random_projection::learn(correlated_plane, DimensionReducer, [n_components(1), random_seed(29)]),
         random_projection::export_to_file(correlated_plane, DimensionReducer, reducer, 'random_projection_reducer.pl').

    | ?- logtalk_load('random_projection_reducer.pl'),
         reducer(Reducer),
         random_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 3. For example:

    random_projection_reducer(Encoders, Components, Diagnostics)

Where:

- `Encoders`: List of continuous attribute encoders storing attribute name, mean, and scale.

- `Components`: List of sampled projection vectors in component order.

- `Diagnostics`: Learned reducer metadata including the effective training options and reproducibility 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. Johnson, W. B. and Lindenstrauss, J. (1984) - “Extensions of Lipschitz mappings into a Hilbert space”.

2. Achlioptas, D. (2003) - “Database-friendly random projections: Johnson-Lindenstrauss with binary coins”.