pyrcn.datasets

The pyrcn.datasets includes datasets for reference experiments.

pyrcn.datasets.load_digits(*, n_class: Union[int, integer] = 10, return_X_y: bool = False, as_frame: bool = False, as_sequence: bool = False) → Union[Bunch, tuple]

Load and return the digits dataset (classification).

Each datapoint is a 8x8 image of a digit. ================= ============== Classes 10 Samples per class ~180 Samples total 1797 Dimensionality 64 Features integers 0-16 ================= ============== Read more in the User Guide.

Parameters

  • n_class (Union[int, np.integer], default=10) – The number of classes to return. Between 0 and 10.

  • return_X_y (bool, default=False) – If True, returns (data, target) instead of a Bunch object. See below for more information about the data and target object. .. versionadded:: 0.18

  • as_frame (bool, default=False) – If True, the data is a pandas DataFrame including columns with appropriate dtypes (numeric). The target is a pandas DataFrame or Series depending on the number of target columns. If return_X_y is True, then (data, target) will be pandas DataFrames or Series as described below. .. versionadded:: 0.23

Returns

  • data (Bunch) – Dictionary-like object, with the following attributes. data : {ndarray, dataframe} of shape (1797, 64)

    The flattened data matrix. If as_frame=True, data will be a pandas DataFrame.

    target: {ndarray, Series} of shape (1797,)

    The classification target. If as_frame=True, target will be a pandas Series.

    feature_names: list

    The names of the dataset columns.

    target_names: list

    The names of target classes. .. versionadded:: 0.20

    frame: DataFrame of shape (1797, 65)

    Only present when as_frame=True. DataFrame with data and target. .. versionadded:: 0.23

    images: {ndarray} of shape (1797, 8, 8)

    The raw image data.

    DESCR: str

    The full description of the dataset.

  • (data, target) (tuple if return_X_y is True)

pyrcn.datasets.lorenz(n_timesteps: int, n_future: int = 1, sigma: float = 10.0, rho: float = 28.0, beta: float = 2.6666666666666665, x_0: Union[List, ndarray] = [1.0, 1.0, 1.0], h: float = 0.03, **kwargs: Dict) → Tuple[ndarray, ndarray]

Lorenz time-series.

Lorenz timeseries 1 2, computed from the Lorenz delayed differential equation: .. math:

\\frac{dx}{dt} = \\sigma(y - x)
\\frac{dy}{dt} = x(\\rho - z) - y
\\frac{dz}{dt} = xy - \\beta z
Parameters

  • n_timesteps (int) – Number of timesteps to compute.

  • n_future (int, default = 1) – distance between input and target samples.

  • sigma (float, default = 10) – \(\\sigma\) parameter of the system.

  • rho (float, default = 28.) – \(\\rho\) parameter of the equation.

  • beta (float, default = :math: \frac{8}{3}) – \(\\beta\) parameter of the equation.

  • x_0 (Union[List, np.ndarray], default = [1.0, 1.0, 1.0]) – Initial condition of the timeseries.

  • h (float, default = 0.03) – Discretization step for the Runge-Kutta method. Can be assimilated to the number of discrete point computed per timestep.

Returns

Lorenz attractor timeseries.

Return type

np.ndarray

Note

This code was inspired and adapted from the ReservoirPy library 3.

References

1

E. N. Lorenz, ‘Deterministic Nonperiodic Flow’, Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, Mar. 1963, doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

2

‘Lorenz system <https://en.wikipedia.org/wiki/Lorenz_system>’_ on Wikipedia.

3

Trouvain et al., ‘ReservoirPy: an Efficient and User-Friendly Library to Design Echo State Networks’, In International Conference on Artificial Neural Networks (pp. 494-505). Springer, Cham.

pyrcn.datasets.mackey_glass(n_timesteps: int, n_future: int = 1, tau: int = 17, beta: float = 0.2, gamma: float = 0.1, n: int = 10, x_0: float = 1.2, h: float = 1.0, random_state: Optional[Union[int, RandomState]] = 42) → Tuple[ndarray, ndarray]

Mackey-Glass time-series.

Mackey-Glass timeseries 4 5, computed from the Mackey-Glass delayed differential equation: .. math:

\\frac{dx}{dt} = \\beta\\frac{x(t-\\tau)}{1+x(t-\\tau)^n}-\\gamma x(t)
Parameters

  • n_timesteps (int) – Number of timesteps to compute.

  • n_future (int, default = 1) – distance between input and target samples.

  • tau (int, default = 17) – Time delay \(\\tau\) of the Mackey-Glass equation. Other values can strongly change the chaotic behaviour of the timeseries.

  • beta (float, default = 0.2) – \(\\beta\) parameter of the equation.

  • gamma (float, default = 0.1) – \(\\gamma\) parameter of the equation.

  • n (int, default = 10) – \(n\) parameter of the equation.

  • x_0 (float, default = 1.2) – Initial condition of the timeseries.

  • h (float, default = 1.0) – Discretization step for the Runge-Kutta method. Can be assimilated to the number of discrete point computed per timestep.

  • random_state (Union[int, np.random.RandomState, None], default=42) – Random state seed for reproducibility.

Returns

Mackey-Glass timeseries.

Return type

np.ndarray

Note

This code was inspired and adapted from the ReservoirPy library 6.

References

4

M. C. Mackey and L. Glass, ‘Oscillation and chaos in physiological control systems’, Science, vol. 197, no. 4300, pp. 287–289, Jul. 1977, doi: 10.1126/science.267326.

5

‘Mackey-Glass equation <http://www.scholarpedia.org/article/Mackey-Glass_equation>’_ on Scholarpedia.

6

Trouvain et al., ‘ReservoirPy: an Efficient and User-Friendly Library to Design Echo State Networks’, In International Conference on Artificial Neural Networks (pp. 494-505). Springer, Cham.