#!/usr/bin/env python
# -*- coding: utf-8 -*-
# The MIT License (MIT)
# Copyright (c) 2017 Juan Cabral
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
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# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# =============================================================================
# FUTURE
# =============================================================================
from __future__ import unicode_literals
# =============================================================================
# DOC
# =============================================================================
__doc__ = """"""
# =============================================================================
# IMPORTS
# =============================================================================
import numpy as np
from statsmodels.tsa import stattools
from .core import Extractor
# =============================================================================
# EXTRACTOR CLASS
# =============================================================================
[docs]class AutocorLength(Extractor):
r"""
**Autocor_length**
The autocorrelation, also known as serial correlation, is the
cross-correlation of a signal with itself. Informally, it is the similarity
between observations as a function of the time lag between them. It is a
mathematical tool for finding repeating patterns, such as the presence of
a periodic signal obscured by noise, or identifying the missing fundamental
frequency in a signal implied by its harmonic frequencies.
For an observed series :math:`y_1, y_2,\dots,y_T` with sample mean
:math:`\bar{y}`, the sample lag :math:`-h` autocorrelation is given by:
.. math::
\rho_h = \frac{\sum_{t=h+1}^T (y_t - \bar{y})(y_{t-h}-\bar{y})}
{\sum_{t=1}^T (y_t - \bar{y})^2}
Since the autocorrelation fuction of a light curve is given by a vector and
we can only return one value as a feature, we define the length of the
autocorrelation function where its value is smaller than :math:`e^{-1}` .
References
----------
.. [kim2011quasi] Kim, D. W., Protopapas, P., Byun, Y. I., Alcock, C.,
Khardon, R., & Trichas, M. (2011). Quasi-stellar object selection
algorithm using time variability and machine learning: Selection of
1620 quasi-stellar object candidates from MACHO Large Magellanic Cloud
database. The Astrophysical Journal, 735(2), 68.
Doi:10.1088/0004-637X/735/2/68.
"""
data = ['magnitude']
features = ['Autocor_length']
params = {"nlags": 100}
[docs] def fit(self, magnitude, nlags):
AC = stattools.acf(magnitude, nlags=nlags)
k = next((index for index, value in
enumerate(AC) if value < np.exp(-1)), None)
while k is None:
nlags = nlags + 100
AC = stattools.acf(magnitude, nlags=nlags)
k = next((index for index, value in
enumerate(AC) if value < np.exp(-1)), None)
return {'Autocor_length': k}
