"""Code for Singular Spectrum Analysis."""
# Author: Johann Faouzi <johann.faouzi@gmail.com>
# License: BSD-3-Clause
import numpy as np
from math import ceil
from numba import njit, prange
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.utils.validation import check_array
from ..utils.utils import _windowed_view
@njit
def _outer_dot(v, X, n_samples, window_size, n_windows):
X_new = np.empty((n_samples, window_size, window_size, n_windows))
for i in prange(n_samples):
for j in prange(window_size):
X_new[i, j] = np.dot(np.outer(v[i, :, j], v[i, :, j]), X[i])
return X_new
@njit
def _diagonal_averaging(X, n_samples, n_timestamps, window_size,
n_windows, grouping_size, gap):
X_new = np.empty((n_samples, grouping_size, n_timestamps))
first_row = [(0, col) for col in range(n_windows)]
last_col = [(row, n_windows - 1) for row in range(1, window_size)]
indices = first_row + last_col
for i in prange(n_samples):
for group in prange(grouping_size):
for (j, k) in indices:
X_new[i, group, j + k] = np.diag(
X[i, group, :, ::-1], gap - j - k - 1
).mean()
return X_new
[docs]class SingularSpectrumAnalysis(BaseEstimator, TransformerMixin):
"""Singular Spectrum Analysis.
Parameters
----------
window_size : int or float (default = 4)
Size of the sliding window (i.e. the size of each word). If float, it
represents the percentage of the size of each time series and must be
between 0 and 1. The window size will be computed as
``max(2, ceil(window_size * n_timestamps))``.
groups : None, int or array-like (default = None)
The way the elementary matrices are grouped. If None, no grouping is
performed. If an integer, it represents the number of groups and the
bounds of the groups are computed as
``np.linspace(0, window_size, groups + 1).astype('int64')``.
If array-like, each element must be array-like and contain the indices
for each group.
References
----------
.. [1] N. Golyandina, and A. Zhigljavsky, "Singular Spectrum Analysis for
Time Series". Springer-Verlag Berlin Heidelberg (2013).
Examples
--------
>>> from pyts.datasets import load_gunpoint
>>> from pyts.decomposition import SingularSpectrumAnalysis
>>> X, _, _, _ = load_gunpoint(return_X_y=True)
>>> transformer = SingularSpectrumAnalysis(window_size=5)
>>> X_new = transformer.transform(X)
>>> X_new.shape
(50, 5, 150)
"""
[docs] def __init__(self, window_size=4, groups=None):
self.window_size = window_size
self.groups = groups
[docs] def fit(self, X=None, y=None):
"""Pass.
Parameters
----------
X
ignored
y
Ignored
Returns
-------
self : object
"""
return self
def _grouping(self, X, n_samples, window_size, n_windows):
if self.groups is None:
grouping_size = window_size
X_new = X
elif isinstance(self.groups, int):
grouping = np.linspace(0, window_size,
self.groups + 1).astype('int64')
grouping_size = len(grouping) - 1
X_new = np.zeros((n_samples, grouping_size,
window_size, n_windows))
for i, (j, k) in enumerate(zip(grouping[:-1], grouping[1:])):
X_new[:, i] = X[:, j:k].sum(axis=1)
else:
grouping_size = len(self.groups)
X_new = np.zeros((n_samples, grouping_size,
window_size, n_windows))
for i, group in enumerate(self.groups):
X_new[:, i] = X[:, group].sum(axis=1)
return X_new, grouping_size
def _check_params(self, n_timestamps):
if not isinstance(self.window_size,
(int, np.integer, float, np.floating)):
raise TypeError("'window_size' must be an integer or a float.")
if isinstance(self.window_size, (int, np.integer)):
if not 2 <= self.window_size <= n_timestamps:
raise ValueError(
"If 'window_size' is an integer, it must be greater "
"than or equal to 2 and lower than or equal to "
"n_timestamps (got {0}).".format(self.window_size)
)
window_size = self.window_size
else:
if not 0 < self.window_size <= 1:
raise ValueError(
"If 'window_size' is a float, it must be greater "
"than 0 and lower than or equal to 1 "
"(got {0}).".format(self.window_size)
)
window_size = max(2, ceil(self.window_size * n_timestamps))
if not (self.groups is None
or isinstance(self.groups, (int, list, tuple, np.ndarray))):
raise TypeError("'groups' must be either None, an integer "
"or array-like.")
if isinstance(self.groups, (int, np.integer)):
if not 1 <= self.groups <= self.window_size:
raise ValueError(
"If 'groups' is an integer, it must be greater than or "
"equal to 1 and lower than or equal to 'window_size'."
)
if isinstance(self.groups, (list, tuple, np.ndarray)):
idx = np.concatenate(self.groups)
diff = np.setdiff1d(idx, np.arange(self.window_size))
flat_list = [item for group in self.groups for item in group]
if ((diff.size > 0)
or not (all(isinstance(x, (int, np.integer))
for x in flat_list))):
raise ValueError(
"If 'groups' is array-like, all the values in 'groups' "
"must be integers between 0 and ('window_size' - 1)."
)
return window_size
