Intelegentny_Pszczelarz/.venv/Lib/site-packages/sklearn/neighbors/_nca.py
2023-06-19 00:49:18 +02:00

520 lines
19 KiB
Python

"""
Neighborhood Component Analysis
"""
# Authors: William de Vazelhes <wdevazelhes@gmail.com>
# John Chiotellis <ioannis.chiotellis@in.tum.de>
# License: BSD 3 clause
from warnings import warn
from numbers import Integral, Real
import numpy as np
import sys
import time
from scipy.optimize import minimize
from ..utils.extmath import softmax
from ..metrics import pairwise_distances
from ..base import BaseEstimator, TransformerMixin, ClassNamePrefixFeaturesOutMixin
from ..preprocessing import LabelEncoder
from ..decomposition import PCA
from ..utils.multiclass import check_classification_targets
from ..utils.random import check_random_state
from ..utils.validation import check_is_fitted, check_array
from ..utils._param_validation import Interval, StrOptions
from ..exceptions import ConvergenceWarning
class NeighborhoodComponentsAnalysis(
ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator
):
"""Neighborhood Components Analysis.
Neighborhood Component Analysis (NCA) is a machine learning algorithm for
metric learning. It learns a linear transformation in a supervised fashion
to improve the classification accuracy of a stochastic nearest neighbors
rule in the transformed space.
Read more in the :ref:`User Guide <nca>`.
Parameters
----------
n_components : int, default=None
Preferred dimensionality of the projected space.
If None it will be set to `n_features`.
init : {'auto', 'pca', 'lda', 'identity', 'random'} or ndarray of shape \
(n_features_a, n_features_b), default='auto'
Initialization of the linear transformation. Possible options are
`'auto'`, `'pca'`, `'lda'`, `'identity'`, `'random'`, and a numpy
array of shape `(n_features_a, n_features_b)`.
- `'auto'`
Depending on `n_components`, the most reasonable initialization
will be chosen. If `n_components <= n_classes` we use `'lda'`, as
it uses labels information. If not, but
`n_components < min(n_features, n_samples)`, we use `'pca'`, as
it projects data in meaningful directions (those of higher
variance). Otherwise, we just use `'identity'`.
- `'pca'`
`n_components` principal components of the inputs passed
to :meth:`fit` will be used to initialize the transformation.
(See :class:`~sklearn.decomposition.PCA`)
- `'lda'`
`min(n_components, n_classes)` most discriminative
components of the inputs passed to :meth:`fit` will be used to
initialize the transformation. (If `n_components > n_classes`,
the rest of the components will be zero.) (See
:class:`~sklearn.discriminant_analysis.LinearDiscriminantAnalysis`)
- `'identity'`
If `n_components` is strictly smaller than the
dimensionality of the inputs passed to :meth:`fit`, the identity
matrix will be truncated to the first `n_components` rows.
- `'random'`
The initial transformation will be a random array of shape
`(n_components, n_features)`. Each value is sampled from the
standard normal distribution.
- numpy array
`n_features_b` must match the dimensionality of the inputs passed
to :meth:`fit` and n_features_a must be less than or equal to that.
If `n_components` is not `None`, `n_features_a` must match it.
warm_start : bool, default=False
If `True` and :meth:`fit` has been called before, the solution of the
previous call to :meth:`fit` is used as the initial linear
transformation (`n_components` and `init` will be ignored).
max_iter : int, default=50
Maximum number of iterations in the optimization.
tol : float, default=1e-5
Convergence tolerance for the optimization.
callback : callable, default=None
If not `None`, this function is called after every iteration of the
optimizer, taking as arguments the current solution (flattened
transformation matrix) and the number of iterations. This might be
useful in case one wants to examine or store the transformation
found after each iteration.
verbose : int, default=0
If 0, no progress messages will be printed.
If 1, progress messages will be printed to stdout.
If > 1, progress messages will be printed and the `disp`
parameter of :func:`scipy.optimize.minimize` will be set to
`verbose - 2`.
random_state : int or numpy.RandomState, default=None
A pseudo random number generator object or a seed for it if int. If
`init='random'`, `random_state` is used to initialize the random
transformation. If `init='pca'`, `random_state` is passed as an
argument to PCA when initializing the transformation. Pass an int
for reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
Attributes
----------
components_ : ndarray of shape (n_components, n_features)
The linear transformation learned during fitting.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
n_iter_ : int
Counts the number of iterations performed by the optimizer.
random_state_ : numpy.RandomState
Pseudo random number generator object used during initialization.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
sklearn.discriminant_analysis.LinearDiscriminantAnalysis : Linear
Discriminant Analysis.
sklearn.decomposition.PCA : Principal component analysis (PCA).
References
----------
.. [1] J. Goldberger, G. Hinton, S. Roweis, R. Salakhutdinov.
"Neighbourhood Components Analysis". Advances in Neural Information
Processing Systems. 17, 513-520, 2005.
http://www.cs.nyu.edu/~roweis/papers/ncanips.pdf
.. [2] Wikipedia entry on Neighborhood Components Analysis
https://en.wikipedia.org/wiki/Neighbourhood_components_analysis
Examples
--------
>>> from sklearn.neighbors import NeighborhoodComponentsAnalysis
>>> from sklearn.neighbors import KNeighborsClassifier
>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import train_test_split
>>> X, y = load_iris(return_X_y=True)
>>> X_train, X_test, y_train, y_test = train_test_split(X, y,
... stratify=y, test_size=0.7, random_state=42)
>>> nca = NeighborhoodComponentsAnalysis(random_state=42)
>>> nca.fit(X_train, y_train)
NeighborhoodComponentsAnalysis(...)
>>> knn = KNeighborsClassifier(n_neighbors=3)
>>> knn.fit(X_train, y_train)
KNeighborsClassifier(...)
>>> print(knn.score(X_test, y_test))
0.933333...
>>> knn.fit(nca.transform(X_train), y_train)
KNeighborsClassifier(...)
>>> print(knn.score(nca.transform(X_test), y_test))
0.961904...
"""
_parameter_constraints: dict = {
"n_components": [
Interval(Integral, 1, None, closed="left"),
None,
],
"init": [
StrOptions({"auto", "pca", "lda", "identity", "random"}),
np.ndarray,
],
"warm_start": ["boolean"],
"max_iter": [Interval(Integral, 1, None, closed="left")],
"tol": [Interval(Real, 0, None, closed="left")],
"callback": [callable, None],
"verbose": ["verbose"],
"random_state": ["random_state"],
}
def __init__(
self,
n_components=None,
*,
init="auto",
warm_start=False,
max_iter=50,
tol=1e-5,
callback=None,
verbose=0,
random_state=None,
):
self.n_components = n_components
self.init = init
self.warm_start = warm_start
self.max_iter = max_iter
self.tol = tol
self.callback = callback
self.verbose = verbose
self.random_state = random_state
def fit(self, X, y):
"""Fit the model according to the given training data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The training samples.
y : array-like of shape (n_samples,)
The corresponding training labels.
Returns
-------
self : object
Fitted estimator.
"""
self._validate_params()
# Validate the inputs X and y, and converts y to numerical classes.
X, y = self._validate_data(X, y, ensure_min_samples=2)
check_classification_targets(y)
y = LabelEncoder().fit_transform(y)
# Check the preferred dimensionality of the projected space
if self.n_components is not None and self.n_components > X.shape[1]:
raise ValueError(
"The preferred dimensionality of the "
f"projected space `n_components` ({self.n_components}) cannot "
"be greater than the given data "
f"dimensionality ({X.shape[1]})!"
)
# If warm_start is enabled, check that the inputs are consistent
if (
self.warm_start
and hasattr(self, "components_")
and self.components_.shape[1] != X.shape[1]
):
raise ValueError(
f"The new inputs dimensionality ({X.shape[1]}) does not "
"match the input dimensionality of the "
f"previously learned transformation ({self.components_.shape[1]})."
)
# Check how the linear transformation should be initialized
init = self.init
if isinstance(init, np.ndarray):
init = check_array(init)
# Assert that init.shape[1] = X.shape[1]
if init.shape[1] != X.shape[1]:
raise ValueError(
f"The input dimensionality ({init.shape[1]}) of the given "
"linear transformation `init` must match the "
f"dimensionality of the given inputs `X` ({X.shape[1]})."
)
# Assert that init.shape[0] <= init.shape[1]
if init.shape[0] > init.shape[1]:
raise ValueError(
f"The output dimensionality ({init.shape[0]}) of the given "
"linear transformation `init` cannot be "
f"greater than its input dimensionality ({init.shape[1]})."
)
# Assert that self.n_components = init.shape[0]
if self.n_components is not None and self.n_components != init.shape[0]:
raise ValueError(
"The preferred dimensionality of the "
f"projected space `n_components` ({self.n_components}) does"
" not match the output dimensionality of "
"the given linear transformation "
f"`init` ({init.shape[0]})!"
)
# Initialize the random generator
self.random_state_ = check_random_state(self.random_state)
# Measure the total training time
t_train = time.time()
# Compute a mask that stays fixed during optimization:
same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
# (n_samples, n_samples)
# Initialize the transformation
transformation = np.ravel(self._initialize(X, y, init))
# Create a dictionary of parameters to be passed to the optimizer
disp = self.verbose - 2 if self.verbose > 1 else -1
optimizer_params = {
"method": "L-BFGS-B",
"fun": self._loss_grad_lbfgs,
"args": (X, same_class_mask, -1.0),
"jac": True,
"x0": transformation,
"tol": self.tol,
"options": dict(maxiter=self.max_iter, disp=disp),
"callback": self._callback,
}
# Call the optimizer
self.n_iter_ = 0
opt_result = minimize(**optimizer_params)
# Reshape the solution found by the optimizer
self.components_ = opt_result.x.reshape(-1, X.shape[1])
self._n_features_out = self.components_.shape[1]
# Stop timer
t_train = time.time() - t_train
if self.verbose:
cls_name = self.__class__.__name__
# Warn the user if the algorithm did not converge
if not opt_result.success:
warn(
"[{}] NCA did not converge: {}".format(
cls_name, opt_result.message
),
ConvergenceWarning,
)
print("[{}] Training took {:8.2f}s.".format(cls_name, t_train))
return self
def transform(self, X):
"""Apply the learned transformation to the given data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Data samples.
Returns
-------
X_embedded: ndarray of shape (n_samples, n_components)
The data samples transformed.
Raises
------
NotFittedError
If :meth:`fit` has not been called before.
"""
check_is_fitted(self)
X = self._validate_data(X, reset=False)
return np.dot(X, self.components_.T)
def _initialize(self, X, y, init):
"""Initialize the transformation.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The training samples.
y : array-like of shape (n_samples,)
The training labels.
init : str or ndarray of shape (n_features_a, n_features_b)
The validated initialization of the linear transformation.
Returns
-------
transformation : ndarray of shape (n_components, n_features)
The initialized linear transformation.
"""
transformation = init
if self.warm_start and hasattr(self, "components_"):
transformation = self.components_
elif isinstance(init, np.ndarray):
pass
else:
n_samples, n_features = X.shape
n_components = self.n_components or n_features
if init == "auto":
n_classes = len(np.unique(y))
if n_components <= min(n_features, n_classes - 1):
init = "lda"
elif n_components < min(n_features, n_samples):
init = "pca"
else:
init = "identity"
if init == "identity":
transformation = np.eye(n_components, X.shape[1])
elif init == "random":
transformation = self.random_state_.standard_normal(
size=(n_components, X.shape[1])
)
elif init in {"pca", "lda"}:
init_time = time.time()
if init == "pca":
pca = PCA(
n_components=n_components, random_state=self.random_state_
)
if self.verbose:
print("Finding principal components... ", end="")
sys.stdout.flush()
pca.fit(X)
transformation = pca.components_
elif init == "lda":
from ..discriminant_analysis import LinearDiscriminantAnalysis
lda = LinearDiscriminantAnalysis(n_components=n_components)
if self.verbose:
print("Finding most discriminative components... ", end="")
sys.stdout.flush()
lda.fit(X, y)
transformation = lda.scalings_.T[:n_components]
if self.verbose:
print("done in {:5.2f}s".format(time.time() - init_time))
return transformation
def _callback(self, transformation):
"""Called after each iteration of the optimizer.
Parameters
----------
transformation : ndarray of shape (n_components * n_features,)
The solution computed by the optimizer in this iteration.
"""
if self.callback is not None:
self.callback(transformation, self.n_iter_)
self.n_iter_ += 1
def _loss_grad_lbfgs(self, transformation, X, same_class_mask, sign=1.0):
"""Compute the loss and the loss gradient w.r.t. `transformation`.
Parameters
----------
transformation : ndarray of shape (n_components * n_features,)
The raveled linear transformation on which to compute loss and
evaluate gradient.
X : ndarray of shape (n_samples, n_features)
The training samples.
same_class_mask : ndarray of shape (n_samples, n_samples)
A mask where `mask[i, j] == 1` if `X[i]` and `X[j]` belong
to the same class, and `0` otherwise.
Returns
-------
loss : float
The loss computed for the given transformation.
gradient : ndarray of shape (n_components * n_features,)
The new (flattened) gradient of the loss.
"""
if self.n_iter_ == 0:
self.n_iter_ += 1
if self.verbose:
header_fields = ["Iteration", "Objective Value", "Time(s)"]
header_fmt = "{:>10} {:>20} {:>10}"
header = header_fmt.format(*header_fields)
cls_name = self.__class__.__name__
print("[{}]".format(cls_name))
print(
"[{}] {}\n[{}] {}".format(
cls_name, header, cls_name, "-" * len(header)
)
)
t_funcall = time.time()
transformation = transformation.reshape(-1, X.shape[1])
X_embedded = np.dot(X, transformation.T) # (n_samples, n_components)
# Compute softmax distances
p_ij = pairwise_distances(X_embedded, squared=True)
np.fill_diagonal(p_ij, np.inf)
p_ij = softmax(-p_ij) # (n_samples, n_samples)
# Compute loss
masked_p_ij = p_ij * same_class_mask
p = np.sum(masked_p_ij, axis=1, keepdims=True) # (n_samples, 1)
loss = np.sum(p)
# Compute gradient of loss w.r.t. `transform`
weighted_p_ij = masked_p_ij - p_ij * p
weighted_p_ij_sym = weighted_p_ij + weighted_p_ij.T
np.fill_diagonal(weighted_p_ij_sym, -weighted_p_ij.sum(axis=0))
gradient = 2 * X_embedded.T.dot(weighted_p_ij_sym).dot(X)
# time complexity of the gradient: O(n_components x n_samples x (
# n_samples + n_features))
if self.verbose:
t_funcall = time.time() - t_funcall
values_fmt = "[{}] {:>10} {:>20.6e} {:>10.2f}"
print(
values_fmt.format(
self.__class__.__name__, self.n_iter_, loss, t_funcall
)
)
sys.stdout.flush()
return sign * loss, sign * gradient.ravel()
def _more_tags(self):
return {"requires_y": True}