# `qda_classifier`

Quadratic Discriminant Analysis classifier for continuous datasets using class-specific covariance estimates with diagonal regularization. The implementation learns one quadratic discriminant model per class and predicts the class with the highest class-specific 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#qda_classifier link in a web browser.

## Loading

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

    | ?- logtalk_load(qda_classifier(loader)).

## Testing

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

    | ?- logtalk_load(qda_classifier(tester)).

## Features

- Continuous Datasets: Accepts only datasets whose attributes are all declared as continuous.

- Class-Specific Covariances: Learns one covariance matrix, mean vector, and prior per class.

- Regularized Estimation: Applies configurable diagonal regularization to each class covariance matrix before inversion.

- Feature Scaling: Supports optional z-score scaling of continuous features before training.

- Score Inspection: Provides class 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 each class covariance matrix before inversion (default: `1.0e-6`)

## Usage

### Learning a classifier

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

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

### Making predictions

    | ?- qda_classifier::learn(iris_small, Classifier),
         qda_classifier::predict(Classifier, [sepal_length-5.9, sepal_width-3.0, petal_length-5.1, petal_width-1.8], Class).

    | ?- qda_classifier::learn(iris_small, Classifier),
         qda_classifier::predict_scores(Classifier, [sepal_length-6.4, sepal_width-3.2, petal_length-4.5, petal_width-1.5], Scores).

### Exporting the classifier

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

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

## Classifier representation

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

    qda_classifier(Encoders, Models, Options)

Where:

- `Encoders`: list of continuous feature encoders with learned scaling parameters

- `Models`: list of `class_model(Class, Prior, Mean, Precision, LogDeterminant, Constant)` 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. Hastie, T., Tibshirani, R. and Friedman, J. (2009). “The Elements of Statistical Learning”. Section 4.3.

2. Bishop, C.M. (2006). “Pattern Recognition and Machine Learning”. Section 4.2.

3. Duda, R.O., Hart, P.E. and Stork, D.G. (2001). “Pattern Classification”. Chapter 2.