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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. ↩