.. _library_lda_classifier:

``lda_classifier``
==================

Linear Discriminant Analysis classifier for continuous datasets using a
shared pooled covariance estimate with diagonal regularization. The
implementation learns one linear discriminant function per class and
predicts the class with the highest discriminant score.

The library implements the ``classifier_protocol`` defined in the
``classification_protocols`` library. It provides predicates for
learning a classifier from a dataset, using it to make predictions,
inspecting class scores, and exporting it as a list of predicate clauses
or to a file.

Datasets are represented as objects implementing the
``dataset_protocol`` protocol from the ``classification_protocols``
library. All dataset attributes must be declared as ``continuous``.

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

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

Loading
-------

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

::

   | ?- logtalk_load(lda_classifier(loader)).

Testing
-------

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

::

   | ?- logtalk_load(lda_classifier(tester)).

Features
--------

- **Continuous Datasets**: Accepts only datasets whose attributes are
  all declared as continuous.
- **Pooled Covariance Model**: Learns a shared covariance matrix and
  class-specific means and priors.
- **Regularized Estimation**: Applies configurable diagonal
  regularization to stabilize covariance inversion.
- **Feature Scaling**: Supports optional z-score scaling of continuous
  features before fitting the model.
- **Score Inspection**: Provides discriminant scores for all classes
  using ``predict_scores/3``.
- **Classifier Export**: Learned classifiers can be exported as
  predicate clauses or written to a file.

Options
-------

The ``learn/3`` predicate supports these options:

- ``feature_scaling/1`` - whether to standardize continuous attributes
  before training (default: ``true``)
- ``regularization/1`` - positive diagonal value added to the pooled
  covariance matrix before inversion (default: ``1.0e-6``)

Usage
-----

Learning a classifier
~~~~~~~~~~~~~~~~~~~~~

::

   | ?- lda_classifier::learn(iris_small, Classifier).

   | ?- lda_classifier::learn(iris_small, Classifier, [regularization(1.0e-5)]).

Making predictions
~~~~~~~~~~~~~~~~~~

::

   | ?- lda_classifier::learn(iris_small, Classifier),
        lda_classifier::predict(Classifier, [sepal_length-5.1, sepal_width-3.5, petal_length-1.4, petal_width-0.2], Class).

   | ?- lda_classifier::learn(iris_small, Classifier),
        lda_classifier::predict_scores(Classifier, [sepal_length-6.0, sepal_width-2.9, petal_length-4.5, petal_width-1.5], Scores).

Exporting the classifier
~~~~~~~~~~~~~~~~~~~~~~~~

::

   | ?- lda_classifier::learn(iris_small, Classifier),
        lda_classifier::export_to_clauses(iris_small, Classifier, classify, Clauses).

   | ?- lda_classifier::learn(iris_small, Classifier),
        lda_classifier::export_to_file(iris_small, Classifier, classify, 'classifier.pl').

Classifier representation
-------------------------

The learned classifier is represented as a compound term with the form:

::

   lda_classifier(Encoders, Models, Options)

Where:

- ``Encoders``: list of continuous feature encoders with learned scaling
  parameters
- ``Models``: list of
  ``class_model(Class, Prior, Mean, Weights, Offset)`` terms
- ``Options``: merged training options used to learn the classifier

When exported using ``export_to_clauses/4`` or ``export_to_file/4``,
this classifier 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. Fisher, R.A. (1936). "The use of multiple measurements in taxonomic
   problems".
2. Hastie, T., Tibshirani, R. and Friedman, J. (2009). "The Elements of
   Statistical Learning". Section 4.3.
3. Bishop, C.M. (2006). "Pattern Recognition and Machine Learning".
   Section 4.1.
