549 lines
19 KiB
Python
549 lines
19 KiB
Python
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"""
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Testing for Neighborhood Component Analysis module (sklearn.neighbors.nca)
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"""
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# Authors: William de Vazelhes <wdevazelhes@gmail.com>
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# John Chiotellis <ioannis.chiotellis@in.tum.de>
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# License: BSD 3 clause
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import re
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import numpy as np
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import pytest
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from numpy.testing import assert_array_almost_equal, assert_array_equal
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from scipy.optimize import check_grad
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from sklearn import clone
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from sklearn.datasets import load_iris, make_blobs, make_classification
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from sklearn.exceptions import ConvergenceWarning
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from sklearn.metrics import pairwise_distances
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from sklearn.neighbors import NeighborhoodComponentsAnalysis
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from sklearn.preprocessing import LabelEncoder
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from sklearn.utils import check_random_state
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rng = check_random_state(0)
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# load and shuffle iris dataset
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iris = load_iris()
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perm = rng.permutation(iris.target.size)
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iris_data = iris.data[perm]
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iris_target = iris.target[perm]
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EPS = np.finfo(float).eps
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def test_simple_example():
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"""Test on a simple example.
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Puts four points in the input space where the opposite labels points are
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next to each other. After transform the samples from the same class
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should be next to each other.
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"""
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X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
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y = np.array([1, 0, 1, 0])
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nca = NeighborhoodComponentsAnalysis(
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n_components=2, init="identity", random_state=42
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)
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nca.fit(X, y)
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X_t = nca.transform(X)
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assert_array_equal(pairwise_distances(X_t).argsort()[:, 1], np.array([2, 3, 0, 1]))
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def test_toy_example_collapse_points():
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"""Test on a toy example of three points that should collapse
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We build a simple example: two points from the same class and a point from
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a different class in the middle of them. On this simple example, the new
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(transformed) points should all collapse into one single point. Indeed, the
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objective is 2/(1 + exp(d/2)), with d the euclidean distance between the
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two samples from the same class. This is maximized for d=0 (because d>=0),
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with an objective equal to 1 (loss=-1.).
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"""
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rng = np.random.RandomState(42)
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input_dim = 5
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two_points = rng.randn(2, input_dim)
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X = np.vstack([two_points, two_points.mean(axis=0)[np.newaxis, :]])
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y = [0, 0, 1]
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class LossStorer:
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def __init__(self, X, y):
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self.loss = np.inf # initialize the loss to very high
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# Initialize a fake NCA and variables needed to compute the loss:
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self.fake_nca = NeighborhoodComponentsAnalysis()
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self.fake_nca.n_iter_ = np.inf
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self.X, y = self.fake_nca._validate_data(X, y, ensure_min_samples=2)
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y = LabelEncoder().fit_transform(y)
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self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
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def callback(self, transformation, n_iter):
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"""Stores the last value of the loss function"""
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self.loss, _ = self.fake_nca._loss_grad_lbfgs(
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transformation, self.X, self.same_class_mask, -1.0
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)
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loss_storer = LossStorer(X, y)
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nca = NeighborhoodComponentsAnalysis(random_state=42, callback=loss_storer.callback)
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X_t = nca.fit_transform(X, y)
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print(X_t)
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# test that points are collapsed into one point
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assert_array_almost_equal(X_t - X_t[0], 0.0)
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assert abs(loss_storer.loss + 1) < 1e-10
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def test_finite_differences(global_random_seed):
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"""Test gradient of loss function
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Assert that the gradient is almost equal to its finite differences
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approximation.
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"""
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# Initialize the transformation `M`, as well as `X` and `y` and `NCA`
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rng = np.random.RandomState(global_random_seed)
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X, y = make_classification(random_state=global_random_seed)
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M = rng.randn(rng.randint(1, X.shape[1] + 1), X.shape[1])
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nca = NeighborhoodComponentsAnalysis()
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nca.n_iter_ = 0
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mask = y[:, np.newaxis] == y[np.newaxis, :]
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def fun(M):
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return nca._loss_grad_lbfgs(M, X, mask)[0]
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def grad(M):
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return nca._loss_grad_lbfgs(M, X, mask)[1]
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# compare the gradient to a finite difference approximation
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diff = check_grad(fun, grad, M.ravel())
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assert diff == pytest.approx(0.0, abs=1e-4)
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def test_params_validation():
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# Test that invalid parameters raise value error
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X = np.arange(12).reshape(4, 3)
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y = [1, 1, 2, 2]
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NCA = NeighborhoodComponentsAnalysis
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rng = np.random.RandomState(42)
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init = rng.rand(5, 3)
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msg = (
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f"The output dimensionality ({init.shape[0]}) "
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"of the given linear transformation `init` cannot be "
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f"greater than its input dimensionality ({init.shape[1]})."
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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NCA(init=init).fit(X, y)
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n_components = 10
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msg = (
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"The preferred dimensionality of the projected space "
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f"`n_components` ({n_components}) cannot be greater "
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f"than the given data dimensionality ({X.shape[1]})!"
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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NCA(n_components=n_components).fit(X, y)
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def test_transformation_dimensions():
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X = np.arange(12).reshape(4, 3)
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y = [1, 1, 2, 2]
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# Fail if transformation input dimension does not match inputs dimensions
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transformation = np.array([[1, 2], [3, 4]])
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with pytest.raises(ValueError):
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NeighborhoodComponentsAnalysis(init=transformation).fit(X, y)
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# Fail if transformation output dimension is larger than
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# transformation input dimension
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transformation = np.array([[1, 2], [3, 4], [5, 6]])
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# len(transformation) > len(transformation[0])
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with pytest.raises(ValueError):
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NeighborhoodComponentsAnalysis(init=transformation).fit(X, y)
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# Pass otherwise
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transformation = np.arange(9).reshape(3, 3)
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NeighborhoodComponentsAnalysis(init=transformation).fit(X, y)
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def test_n_components():
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rng = np.random.RandomState(42)
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X = np.arange(12).reshape(4, 3)
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y = [1, 1, 2, 2]
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init = rng.rand(X.shape[1] - 1, 3)
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# n_components = X.shape[1] != transformation.shape[0]
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n_components = X.shape[1]
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nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
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msg = (
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"The preferred dimensionality of the projected space "
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f"`n_components` ({n_components}) does not match the output "
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"dimensionality of the given linear transformation "
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f"`init` ({init.shape[0]})!"
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X, y)
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# n_components > X.shape[1]
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n_components = X.shape[1] + 2
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nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
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msg = (
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"The preferred dimensionality of the projected space "
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f"`n_components` ({n_components}) cannot be greater than "
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f"the given data dimensionality ({X.shape[1]})!"
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X, y)
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# n_components < X.shape[1]
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nca = NeighborhoodComponentsAnalysis(n_components=2, init="identity")
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nca.fit(X, y)
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def test_init_transformation():
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rng = np.random.RandomState(42)
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X, y = make_blobs(n_samples=30, centers=6, n_features=5, random_state=0)
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# Start learning from scratch
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nca = NeighborhoodComponentsAnalysis(init="identity")
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nca.fit(X, y)
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# Initialize with random
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nca_random = NeighborhoodComponentsAnalysis(init="random")
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nca_random.fit(X, y)
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# Initialize with auto
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nca_auto = NeighborhoodComponentsAnalysis(init="auto")
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nca_auto.fit(X, y)
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# Initialize with PCA
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nca_pca = NeighborhoodComponentsAnalysis(init="pca")
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nca_pca.fit(X, y)
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# Initialize with LDA
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nca_lda = NeighborhoodComponentsAnalysis(init="lda")
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nca_lda.fit(X, y)
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init = rng.rand(X.shape[1], X.shape[1])
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nca = NeighborhoodComponentsAnalysis(init=init)
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nca.fit(X, y)
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# init.shape[1] must match X.shape[1]
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init = rng.rand(X.shape[1], X.shape[1] + 1)
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nca = NeighborhoodComponentsAnalysis(init=init)
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msg = (
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f"The input dimensionality ({init.shape[1]}) of the given "
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"linear transformation `init` must match the "
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f"dimensionality of the given inputs `X` ({X.shape[1]})."
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X, y)
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# init.shape[0] must be <= init.shape[1]
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init = rng.rand(X.shape[1] + 1, X.shape[1])
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nca = NeighborhoodComponentsAnalysis(init=init)
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msg = (
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f"The output dimensionality ({init.shape[0]}) of the given "
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"linear transformation `init` cannot be "
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f"greater than its input dimensionality ({init.shape[1]})."
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X, y)
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# init.shape[0] must match n_components
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init = rng.rand(X.shape[1], X.shape[1])
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n_components = X.shape[1] - 2
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nca = NeighborhoodComponentsAnalysis(init=init, n_components=n_components)
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msg = (
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"The preferred dimensionality of the "
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f"projected space `n_components` ({n_components}) "
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"does not match the output dimensionality of the given "
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f"linear transformation `init` ({init.shape[0]})!"
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X, y)
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@pytest.mark.parametrize("n_samples", [3, 5, 7, 11])
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@pytest.mark.parametrize("n_features", [3, 5, 7, 11])
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@pytest.mark.parametrize("n_classes", [5, 7, 11])
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@pytest.mark.parametrize("n_components", [3, 5, 7, 11])
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def test_auto_init(n_samples, n_features, n_classes, n_components):
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# Test that auto choose the init as expected with every configuration
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# of order of n_samples, n_features, n_classes and n_components.
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rng = np.random.RandomState(42)
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nca_base = NeighborhoodComponentsAnalysis(
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init="auto", n_components=n_components, max_iter=1, random_state=rng
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)
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if n_classes >= n_samples:
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pass
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# n_classes > n_samples is impossible, and n_classes == n_samples
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# throws an error from lda but is an absurd case
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else:
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X = rng.randn(n_samples, n_features)
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y = np.tile(range(n_classes), n_samples // n_classes + 1)[:n_samples]
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if n_components > n_features:
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# this would return a ValueError, which is already tested in
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# test_params_validation
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pass
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else:
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nca = clone(nca_base)
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nca.fit(X, y)
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if n_components <= min(n_classes - 1, n_features):
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nca_other = clone(nca_base).set_params(init="lda")
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elif n_components < min(n_features, n_samples):
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nca_other = clone(nca_base).set_params(init="pca")
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else:
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nca_other = clone(nca_base).set_params(init="identity")
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nca_other.fit(X, y)
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assert_array_almost_equal(nca.components_, nca_other.components_)
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def test_warm_start_validation():
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X, y = make_classification(
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n_samples=30,
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n_features=5,
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n_classes=4,
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n_redundant=0,
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n_informative=5,
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random_state=0,
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)
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nca = NeighborhoodComponentsAnalysis(warm_start=True, max_iter=5)
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nca.fit(X, y)
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X_less_features, y = make_classification(
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n_samples=30,
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n_features=4,
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n_classes=4,
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n_redundant=0,
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n_informative=4,
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random_state=0,
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)
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msg = (
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f"The new inputs dimensionality ({X_less_features.shape[1]}) "
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"does not match the input dimensionality of the previously learned "
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f"transformation ({nca.components_.shape[1]})."
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)
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with pytest.raises(ValueError, match=re.escape(msg)):
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nca.fit(X_less_features, y)
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def test_warm_start_effectiveness():
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# A 1-iteration second fit on same data should give almost same result
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# with warm starting, and quite different result without warm starting.
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nca_warm = NeighborhoodComponentsAnalysis(warm_start=True, random_state=0)
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nca_warm.fit(iris_data, iris_target)
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transformation_warm = nca_warm.components_
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nca_warm.max_iter = 1
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nca_warm.fit(iris_data, iris_target)
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transformation_warm_plus_one = nca_warm.components_
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nca_cold = NeighborhoodComponentsAnalysis(warm_start=False, random_state=0)
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nca_cold.fit(iris_data, iris_target)
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transformation_cold = nca_cold.components_
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nca_cold.max_iter = 1
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||
|
|
nca_cold.fit(iris_data, iris_target)
|
||
|
|
transformation_cold_plus_one = nca_cold.components_
|
||
|
|
|
||
|
|
diff_warm = np.sum(np.abs(transformation_warm_plus_one - transformation_warm))
|
||
|
|
diff_cold = np.sum(np.abs(transformation_cold_plus_one - transformation_cold))
|
||
|
|
assert diff_warm < 3.0, (
|
||
|
|
"Transformer changed significantly after one "
|
||
|
|
"iteration even though it was warm-started."
|
||
|
|
)
|
||
|
|
|
||
|
|
assert diff_cold > diff_warm, (
|
||
|
|
"Cold-started transformer changed less "
|
||
|
|
"significantly than warm-started "
|
||
|
|
"transformer after one iteration."
|
||
|
|
)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
"init_name", ["pca", "lda", "identity", "random", "precomputed"]
|
||
|
|
)
|
||
|
|
def test_verbose(init_name, capsys):
|
||
|
|
# assert there is proper output when verbose = 1, for every initialization
|
||
|
|
# except auto because auto will call one of the others
|
||
|
|
rng = np.random.RandomState(42)
|
||
|
|
X, y = make_blobs(n_samples=30, centers=6, n_features=5, random_state=0)
|
||
|
|
regexp_init = r"... done in \ *\d+\.\d{2}s"
|
||
|
|
msgs = {
|
||
|
|
"pca": "Finding principal components" + regexp_init,
|
||
|
|
"lda": "Finding most discriminative components" + regexp_init,
|
||
|
|
}
|
||
|
|
if init_name == "precomputed":
|
||
|
|
init = rng.randn(X.shape[1], X.shape[1])
|
||
|
|
else:
|
||
|
|
init = init_name
|
||
|
|
nca = NeighborhoodComponentsAnalysis(verbose=1, init=init)
|
||
|
|
nca.fit(X, y)
|
||
|
|
out, _ = capsys.readouterr()
|
||
|
|
|
||
|
|
# check output
|
||
|
|
lines = re.split("\n+", out)
|
||
|
|
# if pca or lda init, an additional line is printed, so we test
|
||
|
|
# it and remove it to test the rest equally among initializations
|
||
|
|
if init_name in ["pca", "lda"]:
|
||
|
|
assert re.match(msgs[init_name], lines[0])
|
||
|
|
lines = lines[1:]
|
||
|
|
assert lines[0] == "[NeighborhoodComponentsAnalysis]"
|
||
|
|
header = "{:>10} {:>20} {:>10}".format("Iteration", "Objective Value", "Time(s)")
|
||
|
|
assert lines[1] == "[NeighborhoodComponentsAnalysis] {}".format(header)
|
||
|
|
assert lines[2] == "[NeighborhoodComponentsAnalysis] {}".format("-" * len(header))
|
||
|
|
for line in lines[3:-2]:
|
||
|
|
# The following regex will match for instance:
|
||
|
|
# '[NeighborhoodComponentsAnalysis] 0 6.988936e+01 0.01'
|
||
|
|
assert re.match(
|
||
|
|
r"\[NeighborhoodComponentsAnalysis\] *\d+ *\d\.\d{6}e"
|
||
|
|
r"[+|-]\d+\ *\d+\.\d{2}",
|
||
|
|
line,
|
||
|
|
)
|
||
|
|
assert re.match(
|
||
|
|
r"\[NeighborhoodComponentsAnalysis\] Training took\ *" r"\d+\.\d{2}s\.",
|
||
|
|
lines[-2],
|
||
|
|
)
|
||
|
|
assert lines[-1] == ""
|
||
|
|
|
||
|
|
|
||
|
|
def test_no_verbose(capsys):
|
||
|
|
# assert by default there is no output (verbose=0)
|
||
|
|
nca = NeighborhoodComponentsAnalysis()
|
||
|
|
nca.fit(iris_data, iris_target)
|
||
|
|
out, _ = capsys.readouterr()
|
||
|
|
# check output
|
||
|
|
assert out == ""
|
||
|
|
|
||
|
|
|
||
|
|
def test_singleton_class():
|
||
|
|
X = iris_data
|
||
|
|
y = iris_target
|
||
|
|
|
||
|
|
# one singleton class
|
||
|
|
singleton_class = 1
|
||
|
|
(ind_singleton,) = np.where(y == singleton_class)
|
||
|
|
y[ind_singleton] = 2
|
||
|
|
y[ind_singleton[0]] = singleton_class
|
||
|
|
|
||
|
|
nca = NeighborhoodComponentsAnalysis(max_iter=30)
|
||
|
|
nca.fit(X, y)
|
||
|
|
|
||
|
|
# One non-singleton class
|
||
|
|
(ind_1,) = np.where(y == 1)
|
||
|
|
(ind_2,) = np.where(y == 2)
|
||
|
|
y[ind_1] = 0
|
||
|
|
y[ind_1[0]] = 1
|
||
|
|
y[ind_2] = 0
|
||
|
|
y[ind_2[0]] = 2
|
||
|
|
|
||
|
|
nca = NeighborhoodComponentsAnalysis(max_iter=30)
|
||
|
|
nca.fit(X, y)
|
||
|
|
|
||
|
|
# Only singleton classes
|
||
|
|
(ind_0,) = np.where(y == 0)
|
||
|
|
(ind_1,) = np.where(y == 1)
|
||
|
|
(ind_2,) = np.where(y == 2)
|
||
|
|
X = X[[ind_0[0], ind_1[0], ind_2[0]]]
|
||
|
|
y = y[[ind_0[0], ind_1[0], ind_2[0]]]
|
||
|
|
|
||
|
|
nca = NeighborhoodComponentsAnalysis(init="identity", max_iter=30)
|
||
|
|
nca.fit(X, y)
|
||
|
|
assert_array_equal(X, nca.transform(X))
|
||
|
|
|
||
|
|
|
||
|
|
def test_one_class():
|
||
|
|
X = iris_data[iris_target == 0]
|
||
|
|
y = iris_target[iris_target == 0]
|
||
|
|
|
||
|
|
nca = NeighborhoodComponentsAnalysis(
|
||
|
|
max_iter=30, n_components=X.shape[1], init="identity"
|
||
|
|
)
|
||
|
|
nca.fit(X, y)
|
||
|
|
assert_array_equal(X, nca.transform(X))
|
||
|
|
|
||
|
|
|
||
|
|
def test_callback(capsys):
|
||
|
|
max_iter = 10
|
||
|
|
|
||
|
|
def my_cb(transformation, n_iter):
|
||
|
|
assert transformation.shape == (iris_data.shape[1] ** 2,)
|
||
|
|
rem_iter = max_iter - n_iter
|
||
|
|
print("{} iterations remaining...".format(rem_iter))
|
||
|
|
|
||
|
|
# assert that my_cb is called
|
||
|
|
nca = NeighborhoodComponentsAnalysis(max_iter=max_iter, callback=my_cb, verbose=1)
|
||
|
|
nca.fit(iris_data, iris_target)
|
||
|
|
out, _ = capsys.readouterr()
|
||
|
|
|
||
|
|
# check output
|
||
|
|
assert "{} iterations remaining...".format(max_iter - 1) in out
|
||
|
|
|
||
|
|
|
||
|
|
def test_expected_transformation_shape():
|
||
|
|
"""Test that the transformation has the expected shape."""
|
||
|
|
X = iris_data
|
||
|
|
y = iris_target
|
||
|
|
|
||
|
|
class TransformationStorer:
|
||
|
|
def __init__(self, X, y):
|
||
|
|
# Initialize a fake NCA and variables needed to call the loss
|
||
|
|
# function:
|
||
|
|
self.fake_nca = NeighborhoodComponentsAnalysis()
|
||
|
|
self.fake_nca.n_iter_ = np.inf
|
||
|
|
self.X, y = self.fake_nca._validate_data(X, y, ensure_min_samples=2)
|
||
|
|
y = LabelEncoder().fit_transform(y)
|
||
|
|
self.same_class_mask = y[:, np.newaxis] == y[np.newaxis, :]
|
||
|
|
|
||
|
|
def callback(self, transformation, n_iter):
|
||
|
|
"""Stores the last value of the transformation taken as input by
|
||
|
|
the optimizer"""
|
||
|
|
self.transformation = transformation
|
||
|
|
|
||
|
|
transformation_storer = TransformationStorer(X, y)
|
||
|
|
cb = transformation_storer.callback
|
||
|
|
nca = NeighborhoodComponentsAnalysis(max_iter=5, callback=cb)
|
||
|
|
nca.fit(X, y)
|
||
|
|
assert transformation_storer.transformation.size == X.shape[1] ** 2
|
||
|
|
|
||
|
|
|
||
|
|
def test_convergence_warning():
|
||
|
|
nca = NeighborhoodComponentsAnalysis(max_iter=2, verbose=1)
|
||
|
|
cls_name = nca.__class__.__name__
|
||
|
|
msg = "[{}] NCA did not converge".format(cls_name)
|
||
|
|
with pytest.warns(ConvergenceWarning, match=re.escape(msg)):
|
||
|
|
nca.fit(iris_data, iris_target)
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.parametrize(
|
||
|
|
"param, value",
|
||
|
|
[
|
||
|
|
("n_components", np.int32(3)),
|
||
|
|
("max_iter", np.int32(100)),
|
||
|
|
("tol", np.float32(0.0001)),
|
||
|
|
],
|
||
|
|
)
|
||
|
|
def test_parameters_valid_types(param, value):
|
||
|
|
# check that no error is raised when parameters have numpy integer or
|
||
|
|
# floating types.
|
||
|
|
nca = NeighborhoodComponentsAnalysis(**{param: value})
|
||
|
|
|
||
|
|
X = iris_data
|
||
|
|
y = iris_target
|
||
|
|
|
||
|
|
nca.fit(X, y)
|
||
|
|
|
||
|
|
|
||
|
|
def test_nca_feature_names_out():
|
||
|
|
"""Check `get_feature_names_out` for `NeighborhoodComponentsAnalysis`."""
|
||
|
|
|
||
|
|
X = iris_data
|
||
|
|
y = iris_target
|
||
|
|
|
||
|
|
est = NeighborhoodComponentsAnalysis().fit(X, y)
|
||
|
|
names_out = est.get_feature_names_out()
|
||
|
|
|
||
|
|
class_name_lower = est.__class__.__name__.lower()
|
||
|
|
expected_names_out = np.array(
|
||
|
|
[f"{class_name_lower}{i}" for i in range(est.components_.shape[1])],
|
||
|
|
dtype=object,
|
||
|
|
)
|
||
|
|
assert_array_equal(names_out, expected_names_out)
|