# 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) – defaults to None

If int, seed is used to seed the random number generator; If RandomState instance, seed is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

• 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 import synth

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

>>> for x, y in dataset.take(5):
...     print(x, y)
{0: 0.7319, 1: 0.5986} 1
{0: 0.8661, 1: 0.6011} 1
{0: 0.8324, 1: 0.2123} 0
{0: 0.5247, 1: 0.4319} 0
{0: 0.2921, 1: 0.3663} 0


## Methods¶

take

Iterate over the k samples.

Parameters

• k (int)

## Notes¶

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.

## References¶

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.