API Reference / datasets / generators / regression /

mexican_hat.py

Mexican hat generator: the Ricker wavelet surface.

Evaluates the negative second derivative of a Gaussian, a radially symmetric surface with a central peak ringed by a trough. Its sharp curvature near the origin makes it a good stress test for smoothers and local regressors.

Classes

MexicanHat

class datasets.generators.regression.mexican_hat.MexicanHat(RegressionGenerator)

Mexican Hat (Ricker wavelet) data generator.

Generates data using the Mexican Hat function, which is the negative second derivative of a Gaussian:

y = \left(1 - \frac{r^2}{\sigma^2}\right) \exp\left(-\frac{r^2}{2\sigma^2}\right)

where r is the distance from the center.

Constructor 
__init__(
    self,
    n_samples: int = 100,
    n_features: int = 2,
    amplitude: float = 1.0,
    sigma: float = 1.0,
    noise: float = 0.0,
    random_state: Optional[int] = None,
)

Parameters

n_samples
int = 100
Number of samples to generate.
n_features
int = 2
Number of features (default: 2 for visualization).
amplitude
float = 1.0
Amplitude of the hat.
sigma
float = 1.0
Width parameter of the Gaussian.
noise
float = 0.0
Standard deviation of Gaussian noise.
random_state
int or None = None
Random seed for reproducibility.
python 
>>> from tuiml.datasets.generators.regression import MexicanHat
>>> gen = MexicanHat(n_samples=1000, sigma=1.0, random_state=0)
>>> data = gen.generate()
>>> data.X.shape
(1000, 2)

Methods

generate (self) -> GeneratedData

Generate Mexican Hat data.

Returns
GeneratedData
Generated dataset with feature array X of shape (n_samples, n_features) and continuous target values y.
get_parameter_schema (cls) -> Dict[str, Any]

Return JSON Schema for constructor parameters.