Radial Basis Functions Features for Time-Series Data

RadialBasisFunctions.py

from __future__ import print_function
import numpy as np


class RadialBasisFunctions(object):
    
    """Radial Basis Functions features for time-series data
    
    Parameters
    ----------
    
    frequency : float
        Frequency of the time series, e.g. 12 for monthly, 52 weekly, etc.
    
    period : float
        Period of the time series, e.g. 362.25 days for a year with daily data.
    
    alpha : float or None
        Scale for the RBF kernels. If None, it defaults to 0.5 * (period/frequency)**2.
    
    centered : bool
        Center RBF kernels.
        
    Examples
    --------

    >>> import numpy as np
    >>> rbf = RadialBasisFunctions(frequency=4, period=365.25)
    >>> x = np.arange(0, 365.25*4)
    >>> rbf.transform(x)
    array([[0.60653066, 0.01111272, 0.01111272, 0.60653066],
           [0.61981325, 0.01186396, 0.01040417, 0.59324805],
           [0.63308293, 0.01266002, 0.00973624, 0.57997802],
           ...,
           [0.56673287, 0.00910696, 0.01350311, 0.64632657],
           [0.57997802, 0.00973624, 0.01266002, 0.63308293],
           [0.59324805, 0.01040417, 0.01186396, 0.61981325]])
    
    """
    
    def __init__(self, frequency, period, alpha=None, centered=True):
        
        self.frequency = frequency
        self.period = period
        self.step = self.period / self.frequency
        self.centered = centered
        
        if alpha is None:
            self.alpha = 0.5 * self.step*self.step
        else:
            self.alpha = 2 * alpha
        
    def _kern(self, x, loc):
        z = x-loc
        return np.exp(-(z*z)/self.alpha)
    
    def transform(self, x):
        
        """Transform the time-series indexes to Radial Basis Functions
        
        Parameters
        ----------
        
        X : array (n_samples,)
            Time-series indexes.
        
        Returns
        -------
        
        array, shape (n_samples, frequency)
            RBF features.
        """
        
        if isinstance(x, (list,)):
            x = np.array(x)
        
        if x.ndim > 1:
            raise TypeError
                
        one_period_earlier = (np.min(x) // self.period - 1) * self.period
        
        if self.centered:
            lower = one_period_earlier + self.step/2
        else:
            lower = one_period_earlier
        
        lower = lower - self.period
        upper = np.max(x) + self.period
        
        out = np.zeros((x.shape[0], self.frequency))
        
        for i,m in enumerate(np.arange(lower, upper, self.step)):
            out[:, i % self.frequency] += self._kern(x, m)
            
        return out


if __name__ == '__main__':
    import doctest
    doctest.testmod()