# `isolation_forest`

This library implements the Extended Isolation Forest (EIF) algorithm for anomaly detection as described by Hariri et al. (2019). The Extended Isolation Forest improves upon the original Isolation Forest algorithm (Liu et al., 2008) by using random hyperplane cuts instead of axis-aligned cuts, eliminating bias artifacts in anomaly scores along coordinate axes.

The algorithm builds an ensemble of isolation trees (iTrees) by recursively partitioning data using random hyperplanes. Anomalous points, being few and different from normal points, require fewer partitions (shorter path lengths) to be isolated. The anomaly score for an instance is computed based on the average path length across all trees in the forest.

Datasets are represented as objects implementing the `dataset_protocol` protocol from the `classifier_protocols` library. See the `test_datasets` directory for examples.

## API documentation

Open the ../../apis/library_index.html#isolation-forest link in a web browser.

## Loading

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

    | ?- logtalk_load(isolation_forest(loader)).

## Testing

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

    | ?- logtalk_load(isolation_forest(tester)).

## Implemented features

- Extended Isolation Forest with random hyperplane cuts: splits are defined by random normal vectors and intercept points drawn from the data range, producing `(x - p) * n =< 0` partitions that generalize to arbitrary orientations

- Configurable extension level: level 0 corresponds to the original axis-aligned Isolation Forest; levels up to `d - 1` (the default) use fully extended random hyperplanes where `d` is the number of dimensions

- Anomaly score computation following Liu et al. (2008): `s(x) = 2^(-E(h(x)) / c(psi))` where `E(h(x))` is the average path length across all trees, `c(psi)` is the average path length of unsuccessful searches in a BST, and `psi` is the subsample size

- Handling of both continuous (numeric) and discrete (categorical) attributes: discrete attributes are mapped to numeric indices based on their position in the attribute value list declared by the dataset

- Handling of missing attribute values (represented using anonymous variables): during tree construction, missing values are replaced with random values drawn from the observed range of the corresponding attribute; during scoring, missing dimensions are excluded from the hyperplane dot product computation so that routing decisions at each tree node are based entirely on the known attribute values

- Configurable parameters via options:

  - `number_of_trees/1` (default: `100`): number of isolation trees

  - `subsample_size/1` (default: `256` or number of instances if smaller): subsample size for each tree

  - `extension_level/1` (default: `d - 1`): controls the dimensionality of the random hyperplane normal vectors

  - `anomaly_threshold/1` (default: `0.5`): threshold for anomaly prediction

- Scoring all dataset instances with results sorted by descending anomaly score for easy identification of top anomalies

- Pretty-printing of learned models with tree depth and node count summaries

## Limitations

- No incremental learning (the forest must be rebuilt from scratch when new examples are added)

- No streaming or online variant

## References

- Liu, F.T., Ting, K.M. and Zhou, Z.-H. (2008). Isolation Forest. Proceedings of the 2008 Eighth IEEE International Conference on Data Mining, 413-422. https://doi.org/10.1109/ICDM.2008.17

- Hariri, S., Kind, M.C. and Brunner, R.J. (2019). Extended Isolation Forest. IEEE Transactions on Knowledge and Data Engineering, 33(4), 1479-1489. https://doi.org/10.1109/TKDE.2019.2947676

## Usage

To learn an isolation forest model from a dataset with default options:

    | ?- isolation_forest::learn(gaussian_anomalies, Model).

To learn with custom options:

    | ?- isolation_forest::learn(gaussian_anomalies, Model, [
             number_of_trees(200),
             subsample_size(128),
             extension_level(1),
             anomaly_threshold(0.6)
         ]).

To compute the anomaly score for a new instance:

    | ?- isolation_forest::learn(gaussian_anomalies, Model),
         isolation_forest::score(Model, [x-0.12, y-0.34], Score).

To predict whether an instance is an anomaly or normal:

    | ?- isolation_forest::learn(gaussian_anomalies, Model),
         isolation_forest::predict(Model, [x-4.50, y-4.20], Prediction).

To compute and rank anomaly scores for all instances in a dataset:

    | ?- isolation_forest::learn(gaussian_anomalies, Model),
         isolation_forest::score_all(gaussian_anomalies, Model, Scores).

The `Scores` list contains `Id-Class-Score` triples sorted by descending anomaly score. This makes it easy to inspect top anomalies:

    | ?- isolation_forest::learn(gaussian_anomalies, Model),
         isolation_forest::score_all(gaussian_anomalies, Model, [Top1, Top2, Top3| _]).

To print a summary of the learned model:

    | ?- isolation_forest::learn(gaussian_anomalies, Model),
         isolation_forest::print_model(Model).

To use the original (non-extended) Isolation Forest, set the extension level to 0:

    | ?- isolation_forest::learn(gaussian_anomalies, Model, [extension_level(0)]).