# `kcenters_clusterer`

k-Centers clusterer. It uses a deterministic farthest-first center selection heuristic. Supports continuous attributes only.

The library implements the `clusterer_protocol` defined in the `clustering_protocols` library. It provides predicates for learning a clusterer from a dataset, assigning new instances to clusters, and exporting the learned clusterer as a list of predicate clauses or to a file.

Datasets are represented as objects implementing the `clustering_dataset_protocol` protocol from the `clustering_protocols` library.

## API documentation

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

## Loading

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

    | ?- logtalk_load(kcenters_clusterer(loader)).

## Testing

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

    | ?- logtalk_load(kcenters_clusterer(tester)).

To run the performance benchmark suite, load the `tester_performance.lgt` file:

    | ?- logtalk_load(kcenters_clusterer(tester_performance)).

## Features

- Continuous Datasets: Accepts datasets containing only continuous attributes.

- Farthest-First Center Selection: Uses a deterministic farthest-first heuristic to choose centers.

- Deterministic Initialization: Supports `first_k` and deterministic `spread` initialization that repeatedly chooses the farthest example from the centers selected so far..

- Distance Metrics: Supports Euclidean and Manhattan distances..

- Optional Feature Scaling: Continuous attributes can be standardized using z-score scaling.

- Rich Training Diagnostics: Learned clusterers report training example count, selected center count, and the center-selection strategy used during learning.

- Portable Export: Learned clusterers can be exported as clauses or files and reused later.

## Options

The following options can be passed to the `learn/3` predicate:

- `k(K)`: Number of clusters to learn. Default is `2`.

- `initialization(Initialization)`: Center initialization strategy. Options: `spread` (default) or `first_k`.

- `distance_metric(Metric)`: Distance metric to use. Options: `euclidean` (default) or `manhattan`.

- `feature_scaling(FeatureScaling)`: Whether to standardize continuous attributes before clustering. Options: `on` (default) or `off`.

## Diagnostics

The `diagnostics/2` predicate returns a list containing:

- `model(kcenters_clusterer)`

- `center_count(Count)`

- `training_example_count(Count)`

- `selection_strategy(Strategy)`

- `options(Options)`

## Clusterer representation

The learned clusterer is represented as a compound term with the functor chosen by the user when exporting the clusterer and arity 4. For example:

    kcenters_clusterer(Encoders, Centers, Options, Diagnostics)

Where:

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

- `Centers`: List of center vectors in cluster-id order.

- `Options`: Effective training options used to learn the clusterer.

- `Diagnostics`: Training diagnostics metadata returned by the `diagnostics/2` predicate.

## References

1. Gonzalez (1985) - “Clustering to minimize the maximum intercluster distance”. Theoretical Computer Science, 38, 293-306.