feature_map.py

import numpy as np
from scipy.special import iv
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.utils.validation import check_is_fitted


class ExpSineSquaredSampler(BaseEstimator, TransformerMixin):
    """
    Approximates feature map of an Exp-Sine-Squared kernel by its Fourier series expansion.
    Exp-Sine-Squared kernel is given by:
        k(x, y) = exp(-2(sin(pi * d(x, y) / periodicity) / length_scale)^2)

    Parameters
    ----------
    length_scale : float
    periodicity : float
    degrees : int
        the number of incorporated terms

    Attributes
    ----------
    weights_ : array, (degrees, )
    coef : array, (degrees, )

    """
    def __init__(self, length_scale=1., periodicity=1., degrees=30):
        self.length_scale = length_scale
        self.periodicity = periodicity
        self.degrees = degrees

    def fit(self, X=None, y=None):
        """
        Parameters
        ----------

        Returns
        -------
        self
        """
        self.weights_ = np.arange(1, self.degrees + 1) * 2 * np.pi / self.periodicity
        self.coef_ = iv(np.arange(1, self.degrees + 1), self.length_scale ** (-2)) \
            / np.exp(self.length_scale ** (-2))
        self.coef_ = np.sqrt(self.coef_)
        return self

    def transform(self, X):
        """
        Parameters
        ----------
        X : (n_samples, [n_features])

        Returns
        -------
        X_new : (n_samples, 2 * degrees * n_features)
        """
        check_is_fitted(self, 'weights_')

        if X.ndim == 1:
            X = X[:, np.newaxis]

        n_samples, n_features = X.shape
        projection = X[:, :, np.newaxis] * self.weights_[np.newaxis, np.newaxis, :]
        X_new = np.concatenate([self.coef_[np.newaxis, np.newaxis, :] * np.cos(projection),
                                self.coef_[np.newaxis, np.newaxis, :] * np.sin(projection)],
                               axis=2)
        X_new = np.reshape(X_new, (n_samples, n_features * 2 * self.degrees))
        return X_new