r"""
.. _sec-costl2:
Least squared deviation
====================================================================================================
Description
----------------------------------------------------------------------------------------------------
This cost function detects mean-shifts in a signal.
Formally, for a signal :math:`\{y_t\}_t` on an interval :math:`I`,
.. math:: c(y_{I}) = \sum_{t\in I} \|y_t - \bar{y}\|_2^2
where :math:`\bar{y}` is the mean of :math:`\{y_t\}_{t\in I}`.
Usage
----------------------------------------------------------------------------------------------------
Start with the usual imports and create a signal.
.. code-block:: python
import numpy as np
import matplotlib.pylab as plt
import ruptures as rpt
# creation of data
n, dim = 500, 3 # number of samples, dimension
n_bkps, sigma = 3, 5 # number of change points, noise standart deviation
signal, bkps = rpt.pw_constant(n, dim, n_bkps, noise_std=sigma)
Then create a :class:`CostL2` instance and print the cost of the sub-signal :code:`signal[50:150]`.
.. code-block:: python
c = rpt.costs.CostL2().fit(signal)
print(c.error(50, 150))
You can also compute the sum of costs for a given list of change points.
.. code-block:: python
print(c.sum_of_costs(bkps))
print(c.sum_of_costs([10, 100, 200, 250, n]))
In order to use this cost class in a change point detection algorithm (inheriting from :class:`BaseEstimator`), either pass a :class:`CostL2` instance (through the argument ``'custom_cost'``) or set :code:`model="l2"`.
.. code-block:: python
c = rpt.costs.CostL2(); algo = rpt.Dynp(custom_cost=c)
# is equivalent to
algo = rpt.Dynp(model="l2")
Code explanation
----------------------------------------------------------------------------------------------------
.. autoclass:: ruptures.costs.CostL2
:members:
:special-members: __init__
"""
from ruptures.costs import NotEnoughPoints
from ruptures.base import BaseCost
[docs]class CostL2(BaseCost):
r"""
Least squared deviation.
"""
model = "l2"
[docs] def __init__(self):
self.signal = None
self.min_size = 2
[docs] def fit(self, signal):
"""Set parameters of the instance.
Args:
signal (array): signal. Shape (n_samples,) or (n_samples, n_features)
Returns:
self
"""
if signal.ndim == 1:
self.signal = signal.reshape(-1, 1)
else:
self.signal = signal
return self
[docs] def error(self, start, end):
"""Return the approximation cost on the segment [start:end].
Args:
start (int): start of the segment
end (int): end of the segment
Returns:
float: segment cost
Raises:
NotEnoughPoints: when the segment is too short (less than ``'min_size'`` samples).
"""
if end - start < self.min_size:
raise NotEnoughPoints
return self.signal[start:end].var(axis=0).sum() * (end - start)