# Hyperplane¶

Hyperplane stream generator.

Generates a problem of prediction class of a rotation hyperplane. It was used as testbed for CVFDT and VFDT in 1.

A hyperplane in d-dimensional space is the set of points $$x$$ that satisfy

$\sum^{d}_{i=1} w_i x_i = w_0 = \sum^{d}_{i=1} w_i$

where $$x_i$$ is the i-th coordinate of $$x$$.

• Examples for which $$\sum^{d}_{i=1} w_i x_i > w_0$$, are labeled positive.

• Examples for which $$\sum^{d}_{i=1} w_i x_i \leq w_0$$, are labeled negative.

Hyperplanes are useful for simulating time-changing concepts because we can change the orientation and position of the hyperplane in a smooth manner by changing the relative size of the weights. We introduce change to this dataset by adding drift to each weighted feature $$w_i = w_i + d \sigma$$, where $$\sigma$$ is the probability that the direction of change is reversed and $$d$$ is the change applied to each example.

## Parameters¶

• seed ('int | None') – defaults to None

Random seed for reproducibility.

• n_features ('int') – defaults to 10

The number of attributes to generate. Higher than 2.

• n_drift_features ('int') – defaults to 2

The number of attributes with drift. Higher than 2.

• mag_change ('float') – defaults to 0.0

Magnitude of the change for every example. From 0.0 to 1.0.

• noise_percentage ('float') – defaults to 0.05

Percentage of noise to add to the data. From 0.0 to 1.0.

• sigma ('float') – defaults to 0.1

Probability that the direction of change is reversed. From 0.0 to 1.0.

## Attributes¶

• desc

Return the description from the docstring.

## Examples¶

>>> from river.datasets import synth

>>> dataset = synth.Hyperplane(seed=42, n_features=2)

>>> for x, y in dataset.take(5):
...     print(x, y)
{0: 0.2750, 1: 0.2232} 0
{0: 0.0869, 1: 0.4219} 1
{0: 0.0265, 1: 0.1988} 0
{0: 0.5892, 1: 0.8094} 0
{0: 0.3402, 1: 0.1554} 0


## Methods¶

take

Iterate over the k samples.

Parameters

• k (int)

The sample generation works as follows: The features are generated with the random number generator, initialized with the seed passed by the user. Then the classification function decides, as a function of the sum of the weighted features and the sum of the weights, whether the instance belongs to class 0 or class 1. The last step is to add noise and generate drift.

1. G. Hulten, L. Spencer, and P. Domingos. Mining time-changing data streams. In KDD'01, pages 97-106, San Francisco, CA, 2001. ACM Press.