# HalfSpaceTrees¶

Half-Space Trees (HST).

Half-space trees are an online variant of isolation forests. They work well when anomalies are spread out. However, they do not work well if anomalies are packed together in windows.

By default, this implementation assumes that each feature has values that are comprised between 0 and 1. If this isn't the case, then you can manually specify the limits via the limits argument. If you do not know the limits in advance, then you can use a preprocessing.MinMaxScaler as an initial preprocessing step.

The current implementation builds the trees the first time the learn_one method is called. Therefore, the first learn_one call might be slow, whereas subsequent calls will be very fast in comparison. In general, the computation time of both learn_one and score_one scales linearly with the number of trees, and exponentially with the height of each tree.

Note that high scores indicate anomalies, whereas low scores indicate normal observations.

## Parameters¶

• n_trees – defaults to 10

Number of trees to use.

• height – defaults to 8

Height of each tree. Note that a tree of height h is made up of h + 1 levels and therefore contains 2 ** (h + 1) - 1 nodes.

• window_size – defaults to 250

Number of observations to use for calculating the mass at each node in each tree.

• limits (Dict[Hashable, Tuple[float, float]]) – defaults to None

Specifies the range of each feature. By default each feature is assumed to be in range [0, 1].

• seed (int) – defaults to None

Random number seed.

## Attributes¶

• size_limit

This is the threshold under which the node search stops during the scoring phase. The value .1 is a magic constant indicated in the original paper.

## Examples¶

>>> from river import anomaly

>>> X = [0.5, 0.45, 0.43, 0.44, 0.445, 0.45, 0.0]
>>> hst = anomaly.HalfSpaceTrees(
...     n_trees=5,
...     height=3,
...     window_size=3,
...     seed=42
... )

>>> for x in X[:3]:
...     hst = hst.learn_one({'x': x})  # Warming up

>>> for x in X:
...     features = {'x': x}
...     hst = hst.learn_one(features)
...     print(f'Anomaly score for x={x:.3f}: {hst.score_one(features):.3f}')
Anomaly score for x=0.500: 0.107
Anomaly score for x=0.450: 0.071
Anomaly score for x=0.430: 0.107
Anomaly score for x=0.440: 0.107
Anomaly score for x=0.445: 0.107
Anomaly score for x=0.450: 0.071
Anomaly score for x=0.000: 0.853


The feature values are all comprised between 0 and 1. This is what is assumed by the model by default. In the following example, we construct a pipeline that scales the data online and ensures that the values of each feature are comprised between 0 and 1.

>>> from river import compose
>>> from river import datasets
>>> from river import metrics
>>> from river import preprocessing

>>> model = compose.Pipeline(
...     preprocessing.MinMaxScaler(),
...     anomaly.HalfSpaceTrees(seed=42)
... )

>>> auc = metrics.ROCAUC()

>>> for x, y in datasets.CreditCard().take(2500):
...     score = model.score_one(x)
...     model = model.learn_one(x)
...     auc = auc.update(y, score)

>>> auc
ROCAUC: 93.94%


## Methods¶

learn_one

Update the model.

Parameters

• x (dict)

Returns

AnomalyDetector: self

score_one

Return an outlier score.

A high score is indicative of an anomaly. A low score corresponds to a normal observation.

Parameters

• x (dict)

Returns

float: An anomaly score. A high score is indicative of an anomaly. A low score corresponds a