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_{i = 1}^{d} w_{i} x_{i} = w_{0} = \sum_{i = 1}^{d} w_{i}

where $x_{i}$ is the i-th coordinate of $x$ .

Examples for which $\sum_{i = 1}^{d} w_{i} x_{i} > w_{0}$ , are labeled positive.
Examples for which $\sum_{i = 1}^{d} w_{i} x_{i} \leq w_{0}$ , 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 $w_{i} = w_{i} + d σ$ , where $σ$ 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)

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¶

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