/usr/lib/python3/dist-packages/sklearn/linear_model/ransac.py is in python3-sklearn 0.17.0-4.
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# Author: Johannes Schönberger
#
# License: BSD 3 clause
import numpy as np
from ..base import BaseEstimator, MetaEstimatorMixin, RegressorMixin, clone
from ..utils import check_random_state, check_array, check_consistent_length
from ..utils.random import sample_without_replacement
from ..utils.validation import check_is_fitted
from .base import LinearRegression
_EPSILON = np.spacing(1)
def _dynamic_max_trials(n_inliers, n_samples, min_samples, probability):
"""Determine number trials such that at least one outlier-free subset is
sampled for the given inlier/outlier ratio.
Parameters
----------
n_inliers : int
Number of inliers in the data.
n_samples : int
Total number of samples in the data.
min_samples : int
Minimum number of samples chosen randomly from original data.
probability : float
Probability (confidence) that one outlier-free sample is generated.
Returns
-------
trials : int
Number of trials.
"""
inlier_ratio = n_inliers / float(n_samples)
nom = max(_EPSILON, 1 - probability)
denom = max(_EPSILON, 1 - inlier_ratio ** min_samples)
if nom == 1:
return 0
if denom == 1:
return float('inf')
return abs(float(np.ceil(np.log(nom) / np.log(denom))))
class RANSACRegressor(BaseEstimator, MetaEstimatorMixin, RegressorMixin):
"""RANSAC (RANdom SAmple Consensus) algorithm.
RANSAC is an iterative algorithm for the robust estimation of parameters
from a subset of inliers from the complete data set. More information can
be found in the general documentation of linear models.
A detailed description of the algorithm can be found in the documentation
of the ``linear_model`` sub-package.
Read more in the :ref:`User Guide <ransac_regression>`.
Parameters
----------
base_estimator : object, optional
Base estimator object which implements the following methods:
* `fit(X, y)`: Fit model to given training data and target values.
* `score(X, y)`: Returns the mean accuracy on the given test data,
which is used for the stop criterion defined by `stop_score`.
Additionally, the score is used to decide which of two equally
large consensus sets is chosen as the better one.
If `base_estimator` is None, then
``base_estimator=sklearn.linear_model.LinearRegression()`` is used for
target values of dtype float.
Note that the current implementation only supports regression
estimators.
min_samples : int (>= 1) or float ([0, 1]), optional
Minimum number of samples chosen randomly from original data. Treated
as an absolute number of samples for `min_samples >= 1`, treated as a
relative number `ceil(min_samples * X.shape[0]`) for
`min_samples < 1`. This is typically chosen as the minimal number of
samples necessary to estimate the given `base_estimator`. By default a
``sklearn.linear_model.LinearRegression()`` estimator is assumed and
`min_samples` is chosen as ``X.shape[1] + 1``.
residual_threshold : float, optional
Maximum residual for a data sample to be classified as an inlier.
By default the threshold is chosen as the MAD (median absolute
deviation) of the target values `y`.
is_data_valid : callable, optional
This function is called with the randomly selected data before the
model is fitted to it: `is_data_valid(X, y)`. If its return value is
False the current randomly chosen sub-sample is skipped.
is_model_valid : callable, optional
This function is called with the estimated model and the randomly
selected data: `is_model_valid(model, X, y)`. If its return value is
False the current randomly chosen sub-sample is skipped.
Rejecting samples with this function is computationally costlier than
with `is_data_valid`. `is_model_valid` should therefore only be used if
the estimated model is needed for making the rejection decision.
max_trials : int, optional
Maximum number of iterations for random sample selection.
stop_n_inliers : int, optional
Stop iteration if at least this number of inliers are found.
stop_score : float, optional
Stop iteration if score is greater equal than this threshold.
stop_probability : float in range [0, 1], optional
RANSAC iteration stops if at least one outlier-free set of the training
data is sampled in RANSAC. This requires to generate at least N
samples (iterations)::
N >= log(1 - probability) / log(1 - e**m)
where the probability (confidence) is typically set to high value such
as 0.99 (the default) and e is the current fraction of inliers w.r.t.
the total number of samples.
residual_metric : callable, optional
Metric to reduce the dimensionality of the residuals to 1 for
multi-dimensional target values ``y.shape[1] > 1``. By default the sum
of absolute differences is used::
lambda dy: np.sum(np.abs(dy), axis=1)
random_state : integer or numpy.RandomState, optional
The generator used to initialize the centers. If an integer is
given, it fixes the seed. Defaults to the global numpy random
number generator.
Attributes
----------
estimator_ : object
Best fitted model (copy of the `base_estimator` object).
n_trials_ : int
Number of random selection trials until one of the stop criteria is
met. It is always ``<= max_trials``.
inlier_mask_ : bool array of shape [n_samples]
Boolean mask of inliers classified as ``True``.
References
----------
.. [1] http://en.wikipedia.org/wiki/RANSAC
.. [2] http://www.cs.columbia.edu/~belhumeur/courses/compPhoto/ransac.pdf
.. [3] http://www.bmva.org/bmvc/2009/Papers/Paper355/Paper355.pdf
"""
def __init__(self, base_estimator=None, min_samples=None,
residual_threshold=None, is_data_valid=None,
is_model_valid=None, max_trials=100,
stop_n_inliers=np.inf, stop_score=np.inf,
stop_probability=0.99, residual_metric=None,
random_state=None):
self.base_estimator = base_estimator
self.min_samples = min_samples
self.residual_threshold = residual_threshold
self.is_data_valid = is_data_valid
self.is_model_valid = is_model_valid
self.max_trials = max_trials
self.stop_n_inliers = stop_n_inliers
self.stop_score = stop_score
self.stop_probability = stop_probability
self.residual_metric = residual_metric
self.random_state = random_state
def fit(self, X, y):
"""Fit estimator using RANSAC algorithm.
Parameters
----------
X : array-like or sparse matrix, shape [n_samples, n_features]
Training data.
y : array-like, shape = [n_samples] or [n_samples, n_targets]
Target values.
Raises
------
ValueError
If no valid consensus set could be found. This occurs if
`is_data_valid` and `is_model_valid` return False for all
`max_trials` randomly chosen sub-samples.
"""
X = check_array(X, accept_sparse='csr')
y = check_array(y, ensure_2d=False)
check_consistent_length(X, y)
if self.base_estimator is not None:
base_estimator = clone(self.base_estimator)
else:
base_estimator = LinearRegression()
if self.min_samples is None:
# assume linear model by default
min_samples = X.shape[1] + 1
elif 0 < self.min_samples < 1:
min_samples = np.ceil(self.min_samples * X.shape[0])
elif self.min_samples >= 1:
if self.min_samples % 1 != 0:
raise ValueError("Absolute number of samples must be an "
"integer value.")
min_samples = self.min_samples
else:
raise ValueError("Value for `min_samples` must be scalar and "
"positive.")
if min_samples > X.shape[0]:
raise ValueError("`min_samples` may not be larger than number "
"of samples ``X.shape[0]``.")
if self.stop_probability < 0 or self.stop_probability > 1:
raise ValueError("`stop_probability` must be in range [0, 1].")
if self.residual_threshold is None:
# MAD (median absolute deviation)
residual_threshold = np.median(np.abs(y - np.median(y)))
else:
residual_threshold = self.residual_threshold
if self.residual_metric is None:
residual_metric = lambda dy: np.sum(np.abs(dy), axis=1)
else:
residual_metric = self.residual_metric
random_state = check_random_state(self.random_state)
try: # Not all estimator accept a random_state
base_estimator.set_params(random_state=random_state)
except ValueError:
pass
n_inliers_best = 0
score_best = np.inf
inlier_mask_best = None
X_inlier_best = None
y_inlier_best = None
# number of data samples
n_samples = X.shape[0]
sample_idxs = np.arange(n_samples)
n_samples, _ = X.shape
for self.n_trials_ in range(1, self.max_trials + 1):
# choose random sample set
subset_idxs = sample_without_replacement(n_samples, min_samples,
random_state=random_state)
X_subset = X[subset_idxs]
y_subset = y[subset_idxs]
# check if random sample set is valid
if (self.is_data_valid is not None
and not self.is_data_valid(X_subset, y_subset)):
continue
# fit model for current random sample set
base_estimator.fit(X_subset, y_subset)
# check if estimated model is valid
if (self.is_model_valid is not None and not
self.is_model_valid(base_estimator, X_subset, y_subset)):
continue
# residuals of all data for current random sample model
y_pred = base_estimator.predict(X)
diff = y_pred - y
if diff.ndim == 1:
diff = diff.reshape(-1, 1)
residuals_subset = residual_metric(diff)
# classify data into inliers and outliers
inlier_mask_subset = residuals_subset < residual_threshold
n_inliers_subset = np.sum(inlier_mask_subset)
# less inliers -> skip current random sample
if n_inliers_subset < n_inliers_best:
continue
if n_inliers_subset == 0:
raise ValueError("No inliers found, possible cause is "
"setting residual_threshold ({0}) too low.".format(
self.residual_threshold))
# extract inlier data set
inlier_idxs_subset = sample_idxs[inlier_mask_subset]
X_inlier_subset = X[inlier_idxs_subset]
y_inlier_subset = y[inlier_idxs_subset]
# score of inlier data set
score_subset = base_estimator.score(X_inlier_subset,
y_inlier_subset)
# same number of inliers but worse score -> skip current random
# sample
if (n_inliers_subset == n_inliers_best
and score_subset < score_best):
continue
# save current random sample as best sample
n_inliers_best = n_inliers_subset
score_best = score_subset
inlier_mask_best = inlier_mask_subset
X_inlier_best = X_inlier_subset
y_inlier_best = y_inlier_subset
# break if sufficient number of inliers or score is reached
if (n_inliers_best >= self.stop_n_inliers
or score_best >= self.stop_score
or self.n_trials_
>= _dynamic_max_trials(n_inliers_best, n_samples,
min_samples,
self.stop_probability)):
break
# if none of the iterations met the required criteria
if inlier_mask_best is None:
raise ValueError(
"RANSAC could not find valid consensus set, because"
" either the `residual_threshold` rejected all the samples or"
" `is_data_valid` and `is_model_valid` returned False for all"
" `max_trials` randomly ""chosen sub-samples. Consider "
"relaxing the ""constraints.")
# estimate final model using all inliers
base_estimator.fit(X_inlier_best, y_inlier_best)
self.estimator_ = base_estimator
self.inlier_mask_ = inlier_mask_best
return self
def predict(self, X):
"""Predict using the estimated model.
This is a wrapper for `estimator_.predict(X)`.
Parameters
----------
X : numpy array of shape [n_samples, n_features]
Returns
-------
y : array, shape = [n_samples] or [n_samples, n_targets]
Returns predicted values.
"""
check_is_fitted(self, 'estimator_')
return self.estimator_.predict(X)
def score(self, X, y):
"""Returns the score of the prediction.
This is a wrapper for `estimator_.score(X, y)`.
Parameters
----------
X : numpy array or sparse matrix of shape [n_samples, n_features]
Training data.
y : array, shape = [n_samples] or [n_samples, n_targets]
Target values.
Returns
-------
z : float
Score of the prediction.
"""
check_is_fitted(self, 'estimator_')
return self.estimator_.score(X, y)
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