# `kmedians_clusterer`

k-Medians clusterer. It uses an iterative median-update algorithm with deterministic initialization. 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#kmedians_clusterer link in a web browser.

## Loading

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

    | ?- logtalk_load(kmedians_clusterer(loader)).

## Testing

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

    | ?- logtalk_load(kmedians_clusterer(tester)).

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

    | ?- logtalk_load(kmedians_clusterer(tester_performance)).

## Features

- Continuous Datasets: Accepts datasets containing only continuous attributes.

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

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

- Manhattan Distance: Uses Manhattan distance for cluster assignment and convergence checks.

- Rich Training Diagnostics: Learned clusterers report training example count, convergence status, iteration count, and final median shift.

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

- Stable Empty-Cluster Handling: Empty clusters keep their previous medians instead of failing.

## Options

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

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

- `maximum_iterations(Iterations)`: Maximum number of median-update iterations. Default is `100`.

- `tolerance(Tolerance)`: Maximum median shift threshold for convergence. Default is `1.0e-6`.

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

- `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(kmedians_clusterer)`

- `median_count(Count)`

- `training_example_count(Count)`

- `convergence(Reason)`

- `iterations(Count)`

- `final_shift(Shift)`

- `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:

    kmedians_clusterer(Encoders, Medians, Options, Diagnostics)

Where:

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

- `Medians`: List of median 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. MacQueen (1967) - “Some Methods for Classification and Analysis of Multivariate Observations”. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability.

2. Kaufman & Rousseeuw (1990) - “Finding Groups in Data: An Introduction to Cluster Analysis”. Wiley.