""" Generate samples of synthetic data sets. """ # Authors: B. Thirion, G. Varoquaux, A. Gramfort, V. Michel, O. Grisel, # G. Louppe, J. Nothman # License: BSD 3 clause import numbers import array from collections.abc import Iterable import numpy as np from scipy import linalg import scipy.sparse as sp from ..preprocessing import MultiLabelBinarizer from ..utils import check_array, check_random_state from ..utils import shuffle as util_shuffle from ..utils.random import sample_without_replacement from ..utils.validation import _deprecate_positional_args def _generate_hypercube(samples, dimensions, rng): """Returns distinct binary samples of length dimensions. """ if dimensions > 30: return np.hstack([rng.randint(2, size=(samples, dimensions - 30)), _generate_hypercube(samples, 30, rng)]) out = sample_without_replacement(2 ** dimensions, samples, random_state=rng).astype(dtype='>u4', copy=False) out = np.unpackbits(out.view('>u1')).reshape((-1, 32))[:, -dimensions:] return out @_deprecate_positional_args def make_classification(n_samples=100, n_features=20, *, n_informative=2, n_redundant=2, n_repeated=0, n_classes=2, n_clusters_per_class=2, weights=None, flip_y=0.01, class_sep=1.0, hypercube=True, shift=0.0, scale=1.0, shuffle=True, random_state=None): """Generate a random n-class classification problem. This initially creates clusters of points normally distributed (std=1) about vertices of an ``n_informative``-dimensional hypercube with sides of length ``2*class_sep`` and assigns an equal number of clusters to each class. It introduces interdependence between these features and adds various types of further noise to the data. Without shuffling, ``X`` horizontally stacks features in the following order: the primary ``n_informative`` features, followed by ``n_redundant`` linear combinations of the informative features, followed by ``n_repeated`` duplicates, drawn randomly with replacement from the informative and redundant features. The remaining features are filled with random noise. Thus, without shuffling, all useful features are contained in the columns ``X[:, :n_informative + n_redundant + n_repeated]``. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=20 The total number of features. These comprise ``n_informative`` informative features, ``n_redundant`` redundant features, ``n_repeated`` duplicated features and ``n_features-n_informative-n_redundant-n_repeated`` useless features drawn at random. n_informative : int, default=2 The number of informative features. Each class is composed of a number of gaussian clusters each located around the vertices of a hypercube in a subspace of dimension ``n_informative``. For each cluster, informative features are drawn independently from N(0, 1) and then randomly linearly combined within each cluster in order to add covariance. The clusters are then placed on the vertices of the hypercube. n_redundant : int, default=2 The number of redundant features. These features are generated as random linear combinations of the informative features. n_repeated : int, default=0 The number of duplicated features, drawn randomly from the informative and the redundant features. n_classes : int, default=2 The number of classes (or labels) of the classification problem. n_clusters_per_class : int, default=2 The number of clusters per class. weights : array-like of shape (n_classes,) or (n_classes - 1,),\ default=None The proportions of samples assigned to each class. If None, then classes are balanced. Note that if ``len(weights) == n_classes - 1``, then the last class weight is automatically inferred. More than ``n_samples`` samples may be returned if the sum of ``weights`` exceeds 1. Note that the actual class proportions will not exactly match ``weights`` when ``flip_y`` isn't 0. flip_y : float, default=0.01 The fraction of samples whose class is assigned randomly. Larger values introduce noise in the labels and make the classification task harder. Note that the default setting flip_y > 0 might lead to less than ``n_classes`` in y in some cases. class_sep : float, default=1.0 The factor multiplying the hypercube size. Larger values spread out the clusters/classes and make the classification task easier. hypercube : bool, default=True If True, the clusters are put on the vertices of a hypercube. If False, the clusters are put on the vertices of a random polytope. shift : float, ndarray of shape (n_features,) or None, default=0.0 Shift features by the specified value. If None, then features are shifted by a random value drawn in [-class_sep, class_sep]. scale : float, ndarray of shape (n_features,) or None, default=1.0 Multiply features by the specified value. If None, then features are scaled by a random value drawn in [1, 100]. Note that scaling happens after shifting. shuffle : bool, default=True Shuffle the samples and the features. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The generated samples. y : ndarray of shape (n_samples,) The integer labels for class membership of each sample. Notes ----- The algorithm is adapted from Guyon [1] and was designed to generate the "Madelon" dataset. References ---------- .. [1] I. Guyon, "Design of experiments for the NIPS 2003 variable selection benchmark", 2003. See Also -------- make_blobs : Simplified variant. make_multilabel_classification : Unrelated generator for multilabel tasks. """ generator = check_random_state(random_state) # Count features, clusters and samples if n_informative + n_redundant + n_repeated > n_features: raise ValueError("Number of informative, redundant and repeated " "features must sum to less than the number of total" " features") # Use log2 to avoid overflow errors if n_informative < np.log2(n_classes * n_clusters_per_class): msg = "n_classes({}) * n_clusters_per_class({}) must be" msg += " smaller or equal 2**n_informative({})={}" raise ValueError(msg.format(n_classes, n_clusters_per_class, n_informative, 2**n_informative)) if weights is not None: if len(weights) not in [n_classes, n_classes - 1]: raise ValueError("Weights specified but incompatible with number " "of classes.") if len(weights) == n_classes - 1: if isinstance(weights, list): weights = weights + [1.0 - sum(weights)] else: weights = np.resize(weights, n_classes) weights[-1] = 1.0 - sum(weights[:-1]) else: weights = [1.0 / n_classes] * n_classes n_useless = n_features - n_informative - n_redundant - n_repeated n_clusters = n_classes * n_clusters_per_class # Distribute samples among clusters by weight n_samples_per_cluster = [ int(n_samples * weights[k % n_classes] / n_clusters_per_class) for k in range(n_clusters)] for i in range(n_samples - sum(n_samples_per_cluster)): n_samples_per_cluster[i % n_clusters] += 1 # Initialize X and y X = np.zeros((n_samples, n_features)) y = np.zeros(n_samples, dtype=int) # Build the polytope whose vertices become cluster centroids centroids = _generate_hypercube(n_clusters, n_informative, generator).astype(float, copy=False) centroids *= 2 * class_sep centroids -= class_sep if not hypercube: centroids *= generator.rand(n_clusters, 1) centroids *= generator.rand(1, n_informative) # Initially draw informative features from the standard normal X[:, :n_informative] = generator.randn(n_samples, n_informative) # Create each cluster; a variant of make_blobs stop = 0 for k, centroid in enumerate(centroids): start, stop = stop, stop + n_samples_per_cluster[k] y[start:stop] = k % n_classes # assign labels X_k = X[start:stop, :n_informative] # slice a view of the cluster A = 2 * generator.rand(n_informative, n_informative) - 1 X_k[...] = np.dot(X_k, A) # introduce random covariance X_k += centroid # shift the cluster to a vertex # Create redundant features if n_redundant > 0: B = 2 * generator.rand(n_informative, n_redundant) - 1 X[:, n_informative:n_informative + n_redundant] = \ np.dot(X[:, :n_informative], B) # Repeat some features if n_repeated > 0: n = n_informative + n_redundant indices = ((n - 1) * generator.rand(n_repeated) + 0.5).astype(np.intp) X[:, n:n + n_repeated] = X[:, indices] # Fill useless features if n_useless > 0: X[:, -n_useless:] = generator.randn(n_samples, n_useless) # Randomly replace labels if flip_y >= 0.0: flip_mask = generator.rand(n_samples) < flip_y y[flip_mask] = generator.randint(n_classes, size=flip_mask.sum()) # Randomly shift and scale if shift is None: shift = (2 * generator.rand(n_features) - 1) * class_sep X += shift if scale is None: scale = 1 + 100 * generator.rand(n_features) X *= scale if shuffle: # Randomly permute samples X, y = util_shuffle(X, y, random_state=generator) # Randomly permute features indices = np.arange(n_features) generator.shuffle(indices) X[:, :] = X[:, indices] return X, y @_deprecate_positional_args def make_multilabel_classification(n_samples=100, n_features=20, *, n_classes=5, n_labels=2, length=50, allow_unlabeled=True, sparse=False, return_indicator='dense', return_distributions=False, random_state=None): """Generate a random multilabel classification problem. For each sample, the generative process is: - pick the number of labels: n ~ Poisson(n_labels) - n times, choose a class c: c ~ Multinomial(theta) - pick the document length: k ~ Poisson(length) - k times, choose a word: w ~ Multinomial(theta_c) In the above process, rejection sampling is used to make sure that n is never zero or more than `n_classes`, and that the document length is never zero. Likewise, we reject classes which have already been chosen. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=20 The total number of features. n_classes : int, default=5 The number of classes of the classification problem. n_labels : int, default=2 The average number of labels per instance. More precisely, the number of labels per sample is drawn from a Poisson distribution with ``n_labels`` as its expected value, but samples are bounded (using rejection sampling) by ``n_classes``, and must be nonzero if ``allow_unlabeled`` is False. length : int, default=50 The sum of the features (number of words if documents) is drawn from a Poisson distribution with this expected value. allow_unlabeled : bool, default=True If ``True``, some instances might not belong to any class. sparse : bool, default=False If ``True``, return a sparse feature matrix .. versionadded:: 0.17 parameter to allow *sparse* output. return_indicator : {'dense', 'sparse'} or False, default='dense' If ``'dense'`` return ``Y`` in the dense binary indicator format. If ``'sparse'`` return ``Y`` in the sparse binary indicator format. ``False`` returns a list of lists of labels. return_distributions : bool, default=False If ``True``, return the prior class probability and conditional probabilities of features given classes, from which the data was drawn. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The generated samples. Y : {ndarray, sparse matrix} of shape (n_samples, n_classes) The label sets. Sparse matrix should be of CSR format. p_c : ndarray of shape (n_classes,) The probability of each class being drawn. Only returned if ``return_distributions=True``. p_w_c : ndarray of shape (n_features, n_classes) The probability of each feature being drawn given each class. Only returned if ``return_distributions=True``. """ if n_classes < 1: raise ValueError( "'n_classes' should be an integer greater than 0. Got {} instead." .format(n_classes) ) if length < 1: raise ValueError( "'length' should be an integer greater than 0. Got {} instead." .format(length) ) generator = check_random_state(random_state) p_c = generator.rand(n_classes) p_c /= p_c.sum() cumulative_p_c = np.cumsum(p_c) p_w_c = generator.rand(n_features, n_classes) p_w_c /= np.sum(p_w_c, axis=0) def sample_example(): _, n_classes = p_w_c.shape # pick a nonzero number of labels per document by rejection sampling y_size = n_classes + 1 while (not allow_unlabeled and y_size == 0) or y_size > n_classes: y_size = generator.poisson(n_labels) # pick n classes y = set() while len(y) != y_size: # pick a class with probability P(c) c = np.searchsorted(cumulative_p_c, generator.rand(y_size - len(y))) y.update(c) y = list(y) # pick a non-zero document length by rejection sampling n_words = 0 while n_words == 0: n_words = generator.poisson(length) # generate a document of length n_words if len(y) == 0: # if sample does not belong to any class, generate noise word words = generator.randint(n_features, size=n_words) return words, y # sample words with replacement from selected classes cumulative_p_w_sample = p_w_c.take(y, axis=1).sum(axis=1).cumsum() cumulative_p_w_sample /= cumulative_p_w_sample[-1] words = np.searchsorted(cumulative_p_w_sample, generator.rand(n_words)) return words, y X_indices = array.array('i') X_indptr = array.array('i', [0]) Y = [] for i in range(n_samples): words, y = sample_example() X_indices.extend(words) X_indptr.append(len(X_indices)) Y.append(y) X_data = np.ones(len(X_indices), dtype=np.float64) X = sp.csr_matrix((X_data, X_indices, X_indptr), shape=(n_samples, n_features)) X.sum_duplicates() if not sparse: X = X.toarray() # return_indicator can be True due to backward compatibility if return_indicator in (True, 'sparse', 'dense'): lb = MultiLabelBinarizer(sparse_output=(return_indicator == 'sparse')) Y = lb.fit([range(n_classes)]).transform(Y) elif return_indicator is not False: raise ValueError("return_indicator must be either 'sparse', 'dense' " 'or False.') if return_distributions: return X, Y, p_c, p_w_c return X, Y @_deprecate_positional_args def make_hastie_10_2(n_samples=12000, *, random_state=None): """Generates data for binary classification used in Hastie et al. 2009, Example 10.2. The ten features are standard independent Gaussian and the target ``y`` is defined by:: y[i] = 1 if np.sum(X[i] ** 2) > 9.34 else -1 Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=12000 The number of samples. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 10) The input samples. y : ndarray of shape (n_samples,) The output values. References ---------- .. [1] T. Hastie, R. Tibshirani and J. Friedman, "Elements of Statistical Learning Ed. 2", Springer, 2009. See Also -------- make_gaussian_quantiles : A generalization of this dataset approach. """ rs = check_random_state(random_state) shape = (n_samples, 10) X = rs.normal(size=shape).reshape(shape) y = ((X ** 2.0).sum(axis=1) > 9.34).astype(np.float64, copy=False) y[y == 0.0] = -1.0 return X, y @_deprecate_positional_args def make_regression(n_samples=100, n_features=100, *, n_informative=10, n_targets=1, bias=0.0, effective_rank=None, tail_strength=0.5, noise=0.0, shuffle=True, coef=False, random_state=None): """Generate a random regression problem. The input set can either be well conditioned (by default) or have a low rank-fat tail singular profile. See :func:`make_low_rank_matrix` for more details. The output is generated by applying a (potentially biased) random linear regression model with `n_informative` nonzero regressors to the previously generated input and some gaussian centered noise with some adjustable scale. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=100 The number of features. n_informative : int, default=10 The number of informative features, i.e., the number of features used to build the linear model used to generate the output. n_targets : int, default=1 The number of regression targets, i.e., the dimension of the y output vector associated with a sample. By default, the output is a scalar. bias : float, default=0.0 The bias term in the underlying linear model. effective_rank : int, default=None if not None: The approximate number of singular vectors required to explain most of the input data by linear combinations. Using this kind of singular spectrum in the input allows the generator to reproduce the correlations often observed in practice. if None: The input set is well conditioned, centered and gaussian with unit variance. tail_strength : float, default=0.5 The relative importance of the fat noisy tail of the singular values profile if `effective_rank` is not None. When a float, it should be between 0 and 1. noise : float, default=0.0 The standard deviation of the gaussian noise applied to the output. shuffle : bool, default=True Shuffle the samples and the features. coef : bool, default=False If True, the coefficients of the underlying linear model are returned. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The input samples. y : ndarray of shape (n_samples,) or (n_samples, n_targets) The output values. coef : ndarray of shape (n_features,) or (n_features, n_targets) The coefficient of the underlying linear model. It is returned only if coef is True. """ n_informative = min(n_features, n_informative) generator = check_random_state(random_state) if effective_rank is None: # Randomly generate a well conditioned input set X = generator.randn(n_samples, n_features) else: # Randomly generate a low rank, fat tail input set X = make_low_rank_matrix(n_samples=n_samples, n_features=n_features, effective_rank=effective_rank, tail_strength=tail_strength, random_state=generator) # Generate a ground truth model with only n_informative features being non # zeros (the other features are not correlated to y and should be ignored # by a sparsifying regularizers such as L1 or elastic net) ground_truth = np.zeros((n_features, n_targets)) ground_truth[:n_informative, :] = 100 * generator.rand(n_informative, n_targets) y = np.dot(X, ground_truth) + bias # Add noise if noise > 0.0: y += generator.normal(scale=noise, size=y.shape) # Randomly permute samples and features if shuffle: X, y = util_shuffle(X, y, random_state=generator) indices = np.arange(n_features) generator.shuffle(indices) X[:, :] = X[:, indices] ground_truth = ground_truth[indices] y = np.squeeze(y) if coef: return X, y, np.squeeze(ground_truth) else: return X, y @_deprecate_positional_args def make_circles(n_samples=100, *, shuffle=True, noise=None, random_state=None, factor=.8): """Make a large circle containing a smaller circle in 2d. A simple toy dataset to visualize clustering and classification algorithms. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int or tuple of shape (2,), dtype=int, default=100 If int, it is the total number of points generated. For odd numbers, the inner circle will have one point more than the outer circle. If two-element tuple, number of points in outer circle and inner circle. .. versionchanged:: 0.23 Added two-element tuple. shuffle : bool, default=True Whether to shuffle the samples. noise : float, default=None Standard deviation of Gaussian noise added to the data. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset shuffling and noise. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. factor : float, default=.8 Scale factor between inner and outer circle in the range `(0, 1)`. Returns ------- X : ndarray of shape (n_samples, 2) The generated samples. y : ndarray of shape (n_samples,) The integer labels (0 or 1) for class membership of each sample. """ if factor >= 1 or factor < 0: raise ValueError("'factor' has to be between 0 and 1.") if isinstance(n_samples, numbers.Integral): n_samples_out = n_samples // 2 n_samples_in = n_samples - n_samples_out else: try: n_samples_out, n_samples_in = n_samples except ValueError as e: raise ValueError('`n_samples` can be either an int or ' 'a two-element tuple.') from e generator = check_random_state(random_state) # so as not to have the first point = last point, we set endpoint=False linspace_out = np.linspace(0, 2 * np.pi, n_samples_out, endpoint=False) linspace_in = np.linspace(0, 2 * np.pi, n_samples_in, endpoint=False) outer_circ_x = np.cos(linspace_out) outer_circ_y = np.sin(linspace_out) inner_circ_x = np.cos(linspace_in) * factor inner_circ_y = np.sin(linspace_in) * factor X = np.vstack([np.append(outer_circ_x, inner_circ_x), np.append(outer_circ_y, inner_circ_y)]).T y = np.hstack([np.zeros(n_samples_out, dtype=np.intp), np.ones(n_samples_in, dtype=np.intp)]) if shuffle: X, y = util_shuffle(X, y, random_state=generator) if noise is not None: X += generator.normal(scale=noise, size=X.shape) return X, y @_deprecate_positional_args def make_moons(n_samples=100, *, shuffle=True, noise=None, random_state=None): """Make two interleaving half circles. A simple toy dataset to visualize clustering and classification algorithms. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int or tuple of shape (2,), dtype=int, default=100 If int, the total number of points generated. If two-element tuple, number of points in each of two moons. .. versionchanged:: 0.23 Added two-element tuple. shuffle : bool, default=True Whether to shuffle the samples. noise : float, default=None Standard deviation of Gaussian noise added to the data. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset shuffling and noise. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 2) The generated samples. y : ndarray of shape (n_samples,) The integer labels (0 or 1) for class membership of each sample. """ if isinstance(n_samples, numbers.Integral): n_samples_out = n_samples // 2 n_samples_in = n_samples - n_samples_out else: try: n_samples_out, n_samples_in = n_samples except ValueError as e: raise ValueError('`n_samples` can be either an int or ' 'a two-element tuple.') from e generator = check_random_state(random_state) outer_circ_x = np.cos(np.linspace(0, np.pi, n_samples_out)) outer_circ_y = np.sin(np.linspace(0, np.pi, n_samples_out)) inner_circ_x = 1 - np.cos(np.linspace(0, np.pi, n_samples_in)) inner_circ_y = 1 - np.sin(np.linspace(0, np.pi, n_samples_in)) - .5 X = np.vstack([np.append(outer_circ_x, inner_circ_x), np.append(outer_circ_y, inner_circ_y)]).T y = np.hstack([np.zeros(n_samples_out, dtype=np.intp), np.ones(n_samples_in, dtype=np.intp)]) if shuffle: X, y = util_shuffle(X, y, random_state=generator) if noise is not None: X += generator.normal(scale=noise, size=X.shape) return X, y @_deprecate_positional_args def make_blobs(n_samples=100, n_features=2, *, centers=None, cluster_std=1.0, center_box=(-10.0, 10.0), shuffle=True, random_state=None, return_centers=False): """Generate isotropic Gaussian blobs for clustering. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int or array-like, default=100 If int, it is the total number of points equally divided among clusters. If array-like, each element of the sequence indicates the number of samples per cluster. .. versionchanged:: v0.20 one can now pass an array-like to the ``n_samples`` parameter n_features : int, default=2 The number of features for each sample. centers : int or ndarray of shape (n_centers, n_features), default=None The number of centers to generate, or the fixed center locations. If n_samples is an int and centers is None, 3 centers are generated. If n_samples is array-like, centers must be either None or an array of length equal to the length of n_samples. cluster_std : float or array-like of float, default=1.0 The standard deviation of the clusters. center_box : tuple of float (min, max), default=(-10.0, 10.0) The bounding box for each cluster center when centers are generated at random. shuffle : bool, default=True Shuffle the samples. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. return_centers : bool, default=False If True, then return the centers of each cluster .. versionadded:: 0.23 Returns ------- X : ndarray of shape (n_samples, n_features) The generated samples. y : ndarray of shape (n_samples,) The integer labels for cluster membership of each sample. centers : ndarray of shape (n_centers, n_features) The centers of each cluster. Only returned if ``return_centers=True``. Examples -------- >>> from sklearn.datasets import make_blobs >>> X, y = make_blobs(n_samples=10, centers=3, n_features=2, ... random_state=0) >>> print(X.shape) (10, 2) >>> y array([0, 0, 1, 0, 2, 2, 2, 1, 1, 0]) >>> X, y = make_blobs(n_samples=[3, 3, 4], centers=None, n_features=2, ... random_state=0) >>> print(X.shape) (10, 2) >>> y array([0, 1, 2, 0, 2, 2, 2, 1, 1, 0]) See Also -------- make_classification : A more intricate variant. """ generator = check_random_state(random_state) if isinstance(n_samples, numbers.Integral): # Set n_centers by looking at centers arg if centers is None: centers = 3 if isinstance(centers, numbers.Integral): n_centers = centers centers = generator.uniform(center_box[0], center_box[1], size=(n_centers, n_features)) else: centers = check_array(centers) n_features = centers.shape[1] n_centers = centers.shape[0] else: # Set n_centers by looking at [n_samples] arg n_centers = len(n_samples) if centers is None: centers = generator.uniform(center_box[0], center_box[1], size=(n_centers, n_features)) try: assert len(centers) == n_centers except TypeError as e: raise ValueError("Parameter `centers` must be array-like. " "Got {!r} instead".format(centers)) from e except AssertionError as e: raise ValueError( f"Length of `n_samples` not consistent with number of " f"centers. Got n_samples = {n_samples} and centers = {centers}" ) from e else: centers = check_array(centers) n_features = centers.shape[1] # stds: if cluster_std is given as list, it must be consistent # with the n_centers if (hasattr(cluster_std, "__len__") and len(cluster_std) != n_centers): raise ValueError("Length of `clusters_std` not consistent with " "number of centers. Got centers = {} " "and cluster_std = {}".format(centers, cluster_std)) if isinstance(cluster_std, numbers.Real): cluster_std = np.full(len(centers), cluster_std) X = [] y = [] if isinstance(n_samples, Iterable): n_samples_per_center = n_samples else: n_samples_per_center = [int(n_samples // n_centers)] * n_centers for i in range(n_samples % n_centers): n_samples_per_center[i] += 1 for i, (n, std) in enumerate(zip(n_samples_per_center, cluster_std)): X.append(generator.normal(loc=centers[i], scale=std, size=(n, n_features))) y += [i] * n X = np.concatenate(X) y = np.array(y) if shuffle: total_n_samples = np.sum(n_samples) indices = np.arange(total_n_samples) generator.shuffle(indices) X = X[indices] y = y[indices] if return_centers: return X, y, centers else: return X, y @_deprecate_positional_args def make_friedman1(n_samples=100, n_features=10, *, noise=0.0, random_state=None): """Generate the "Friedman #1" regression problem. This dataset is described in Friedman [1] and Breiman [2]. Inputs `X` are independent features uniformly distributed on the interval [0, 1]. The output `y` is created according to the formula:: y(X) = 10 * sin(pi * X[:, 0] * X[:, 1]) + 20 * (X[:, 2] - 0.5) ** 2 \ + 10 * X[:, 3] + 5 * X[:, 4] + noise * N(0, 1). Out of the `n_features` features, only 5 are actually used to compute `y`. The remaining features are independent of `y`. The number of features has to be >= 5. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=10 The number of features. Should be at least 5. noise : float, default=0.0 The standard deviation of the gaussian noise applied to the output. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset noise. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The input samples. y : ndarray of shape (n_samples,) The output values. References ---------- .. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals of Statistics 19 (1), pages 1-67, 1991. .. [2] L. Breiman, "Bagging predictors", Machine Learning 24, pages 123-140, 1996. """ if n_features < 5: raise ValueError("n_features must be at least five.") generator = check_random_state(random_state) X = generator.rand(n_samples, n_features) y = 10 * np.sin(np.pi * X[:, 0] * X[:, 1]) + 20 * (X[:, 2] - 0.5) ** 2 \ + 10 * X[:, 3] + 5 * X[:, 4] + noise * generator.randn(n_samples) return X, y @_deprecate_positional_args def make_friedman2(n_samples=100, *, noise=0.0, random_state=None): """Generate the "Friedman #2" regression problem. This dataset is described in Friedman [1] and Breiman [2]. Inputs `X` are 4 independent features uniformly distributed on the intervals:: 0 <= X[:, 0] <= 100, 40 * pi <= X[:, 1] <= 560 * pi, 0 <= X[:, 2] <= 1, 1 <= X[:, 3] <= 11. The output `y` is created according to the formula:: y(X) = (X[:, 0] ** 2 + (X[:, 1] * X[:, 2] \ - 1 / (X[:, 1] * X[:, 3])) ** 2) ** 0.5 + noise * N(0, 1). Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. noise : float, default=0.0 The standard deviation of the gaussian noise applied to the output. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset noise. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 4) The input samples. y : ndarray of shape (n_samples,) The output values. References ---------- .. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals of Statistics 19 (1), pages 1-67, 1991. .. [2] L. Breiman, "Bagging predictors", Machine Learning 24, pages 123-140, 1996. """ generator = check_random_state(random_state) X = generator.rand(n_samples, 4) X[:, 0] *= 100 X[:, 1] *= 520 * np.pi X[:, 1] += 40 * np.pi X[:, 3] *= 10 X[:, 3] += 1 y = (X[:, 0] ** 2 + (X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) ** 2) ** 0.5 \ + noise * generator.randn(n_samples) return X, y @_deprecate_positional_args def make_friedman3(n_samples=100, *, noise=0.0, random_state=None): """Generate the "Friedman #3" regression problem. This dataset is described in Friedman [1] and Breiman [2]. Inputs `X` are 4 independent features uniformly distributed on the intervals:: 0 <= X[:, 0] <= 100, 40 * pi <= X[:, 1] <= 560 * pi, 0 <= X[:, 2] <= 1, 1 <= X[:, 3] <= 11. The output `y` is created according to the formula:: y(X) = arctan((X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) \ / X[:, 0]) + noise * N(0, 1). Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. noise : float, default=0.0 The standard deviation of the gaussian noise applied to the output. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset noise. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 4) The input samples. y : ndarray of shape (n_samples,) The output values. References ---------- .. [1] J. Friedman, "Multivariate adaptive regression splines", The Annals of Statistics 19 (1), pages 1-67, 1991. .. [2] L. Breiman, "Bagging predictors", Machine Learning 24, pages 123-140, 1996. """ generator = check_random_state(random_state) X = generator.rand(n_samples, 4) X[:, 0] *= 100 X[:, 1] *= 520 * np.pi X[:, 1] += 40 * np.pi X[:, 3] *= 10 X[:, 3] += 1 y = np.arctan((X[:, 1] * X[:, 2] - 1 / (X[:, 1] * X[:, 3])) / X[:, 0]) \ + noise * generator.randn(n_samples) return X, y @_deprecate_positional_args def make_low_rank_matrix(n_samples=100, n_features=100, *, effective_rank=10, tail_strength=0.5, random_state=None): """Generate a mostly low rank matrix with bell-shaped singular values. Most of the variance can be explained by a bell-shaped curve of width effective_rank: the low rank part of the singular values profile is:: (1 - tail_strength) * exp(-1.0 * (i / effective_rank) ** 2) The remaining singular values' tail is fat, decreasing as:: tail_strength * exp(-0.1 * i / effective_rank). The low rank part of the profile can be considered the structured signal part of the data while the tail can be considered the noisy part of the data that cannot be summarized by a low number of linear components (singular vectors). This kind of singular profiles is often seen in practice, for instance: - gray level pictures of faces - TF-IDF vectors of text documents crawled from the web Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=100 The number of features. effective_rank : int, default=10 The approximate number of singular vectors required to explain most of the data by linear combinations. tail_strength : float, default=0.5 The relative importance of the fat noisy tail of the singular values profile. The value should be between 0 and 1. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The matrix. """ generator = check_random_state(random_state) n = min(n_samples, n_features) # Random (ortho normal) vectors u, _ = linalg.qr(generator.randn(n_samples, n), mode='economic', check_finite=False) v, _ = linalg.qr(generator.randn(n_features, n), mode='economic', check_finite=False) # Index of the singular values singular_ind = np.arange(n, dtype=np.float64) # Build the singular profile by assembling signal and noise components low_rank = ((1 - tail_strength) * np.exp(-1.0 * (singular_ind / effective_rank) ** 2)) tail = tail_strength * np.exp(-0.1 * singular_ind / effective_rank) s = np.identity(n) * (low_rank + tail) return np.dot(np.dot(u, s), v.T) @_deprecate_positional_args def make_sparse_coded_signal(n_samples, *, n_components, n_features, n_nonzero_coefs, random_state=None): """Generate a signal as a sparse combination of dictionary elements. Returns a matrix Y = DX, such as D is (n_features, n_components), X is (n_components, n_samples) and each column of X has exactly n_nonzero_coefs non-zero elements. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int Number of samples to generate n_components : int Number of components in the dictionary n_features : int Number of features of the dataset to generate n_nonzero_coefs : int Number of active (non-zero) coefficients in each sample random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- data : ndarray of shape (n_features, n_samples) The encoded signal (Y). dictionary : ndarray of shape (n_features, n_components) The dictionary with normalized components (D). code : ndarray of shape (n_components, n_samples) The sparse code such that each column of this matrix has exactly n_nonzero_coefs non-zero items (X). """ generator = check_random_state(random_state) # generate dictionary D = generator.randn(n_features, n_components) D /= np.sqrt(np.sum((D ** 2), axis=0)) # generate code X = np.zeros((n_components, n_samples)) for i in range(n_samples): idx = np.arange(n_components) generator.shuffle(idx) idx = idx[:n_nonzero_coefs] X[idx, i] = generator.randn(n_nonzero_coefs) # encode signal Y = np.dot(D, X) return map(np.squeeze, (Y, D, X)) @_deprecate_positional_args def make_sparse_uncorrelated(n_samples=100, n_features=10, *, random_state=None): """Generate a random regression problem with sparse uncorrelated design. This dataset is described in Celeux et al [1]. as:: X ~ N(0, 1) y(X) = X[:, 0] + 2 * X[:, 1] - 2 * X[:, 2] - 1.5 * X[:, 3] Only the first 4 features are informative. The remaining features are useless. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of samples. n_features : int, default=10 The number of features. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The input samples. y : ndarray of shape (n_samples,) The output values. References ---------- .. [1] G. Celeux, M. El Anbari, J.-M. Marin, C. P. Robert, "Regularization in regression: comparing Bayesian and frequentist methods in a poorly informative situation", 2009. """ generator = check_random_state(random_state) X = generator.normal(loc=0, scale=1, size=(n_samples, n_features)) y = generator.normal(loc=(X[:, 0] + 2 * X[:, 1] - 2 * X[:, 2] - 1.5 * X[:, 3]), scale=np.ones(n_samples)) return X, y @_deprecate_positional_args def make_spd_matrix(n_dim, *, random_state=None): """Generate a random symmetric, positive-definite matrix. Read more in the :ref:`User Guide `. Parameters ---------- n_dim : int The matrix dimension. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_dim, n_dim) The random symmetric, positive-definite matrix. See Also -------- make_sparse_spd_matrix """ generator = check_random_state(random_state) A = generator.rand(n_dim, n_dim) U, _, Vt = linalg.svd(np.dot(A.T, A), check_finite=False) X = np.dot(np.dot(U, 1.0 + np.diag(generator.rand(n_dim))), Vt) return X @_deprecate_positional_args def make_sparse_spd_matrix(dim=1, *, alpha=0.95, norm_diag=False, smallest_coef=.1, largest_coef=.9, random_state=None): """Generate a sparse symmetric definite positive matrix. Read more in the :ref:`User Guide `. Parameters ---------- dim : int, default=1 The size of the random matrix to generate. alpha : float, default=0.95 The probability that a coefficient is zero (see notes). Larger values enforce more sparsity. The value should be in the range 0 and 1. norm_diag : bool, default=False Whether to normalize the output matrix to make the leading diagonal elements all 1 smallest_coef : float, default=0.1 The value of the smallest coefficient between 0 and 1. largest_coef : float, default=0.9 The value of the largest coefficient between 0 and 1. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- prec : sparse matrix of shape (dim, dim) The generated matrix. Notes ----- The sparsity is actually imposed on the cholesky factor of the matrix. Thus alpha does not translate directly into the filling fraction of the matrix itself. See Also -------- make_spd_matrix """ random_state = check_random_state(random_state) chol = -np.eye(dim) aux = random_state.rand(dim, dim) aux[aux < alpha] = 0 aux[aux > alpha] = (smallest_coef + (largest_coef - smallest_coef) * random_state.rand(np.sum(aux > alpha))) aux = np.tril(aux, k=-1) # Permute the lines: we don't want to have asymmetries in the final # SPD matrix permutation = random_state.permutation(dim) aux = aux[permutation].T[permutation] chol += aux prec = np.dot(chol.T, chol) if norm_diag: # Form the diagonal vector into a row matrix d = np.diag(prec).reshape(1, prec.shape[0]) d = 1. / np.sqrt(d) prec *= d prec *= d.T return prec @_deprecate_positional_args def make_swiss_roll(n_samples=100, *, noise=0.0, random_state=None): """Generate a swiss roll dataset. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of sample points on the S curve. noise : float, default=0.0 The standard deviation of the gaussian noise. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 3) The points. t : ndarray of shape (n_samples,) The univariate position of the sample according to the main dimension of the points in the manifold. Notes ----- The algorithm is from Marsland [1]. References ---------- .. [1] S. Marsland, "Machine Learning: An Algorithmic Perspective", Chapter 10, 2009. http://seat.massey.ac.nz/personal/s.r.marsland/Code/10/lle.py """ generator = check_random_state(random_state) t = 1.5 * np.pi * (1 + 2 * generator.rand(1, n_samples)) x = t * np.cos(t) y = 21 * generator.rand(1, n_samples) z = t * np.sin(t) X = np.concatenate((x, y, z)) X += noise * generator.randn(3, n_samples) X = X.T t = np.squeeze(t) return X, t @_deprecate_positional_args def make_s_curve(n_samples=100, *, noise=0.0, random_state=None): """Generate an S curve dataset. Read more in the :ref:`User Guide `. Parameters ---------- n_samples : int, default=100 The number of sample points on the S curve. noise : float, default=0.0 The standard deviation of the gaussian noise. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, 3) The points. t : ndarray of shape (n_samples,) The univariate position of the sample according to the main dimension of the points in the manifold. """ generator = check_random_state(random_state) t = 3 * np.pi * (generator.rand(1, n_samples) - 0.5) x = np.sin(t) y = 2.0 * generator.rand(1, n_samples) z = np.sign(t) * (np.cos(t) - 1) X = np.concatenate((x, y, z)) X += noise * generator.randn(3, n_samples) X = X.T t = np.squeeze(t) return X, t @_deprecate_positional_args def make_gaussian_quantiles(*, mean=None, cov=1., n_samples=100, n_features=2, n_classes=3, shuffle=True, random_state=None): r"""Generate isotropic Gaussian and label samples by quantile. This classification dataset is constructed by taking a multi-dimensional standard normal distribution and defining classes separated by nested concentric multi-dimensional spheres such that roughly equal numbers of samples are in each class (quantiles of the :math:`\chi^2` distribution). Read more in the :ref:`User Guide `. Parameters ---------- mean : ndarray of shape (n_features,), default=None The mean of the multi-dimensional normal distribution. If None then use the origin (0, 0, ...). cov : float, default=1.0 The covariance matrix will be this value times the unit matrix. This dataset only produces symmetric normal distributions. n_samples : int, default=100 The total number of points equally divided among classes. n_features : int, default=2 The number of features for each sample. n_classes : int, default=3 The number of classes shuffle : bool, default=True Shuffle the samples. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape (n_samples, n_features) The generated samples. y : ndarray of shape (n_samples,) The integer labels for quantile membership of each sample. Notes ----- The dataset is from Zhu et al [1]. References ---------- .. [1] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost", 2009. """ if n_samples < n_classes: raise ValueError("n_samples must be at least n_classes") generator = check_random_state(random_state) if mean is None: mean = np.zeros(n_features) else: mean = np.array(mean) # Build multivariate normal distribution X = generator.multivariate_normal(mean, cov * np.identity(n_features), (n_samples,)) # Sort by distance from origin idx = np.argsort(np.sum((X - mean[np.newaxis, :]) ** 2, axis=1)) X = X[idx, :] # Label by quantile step = n_samples // n_classes y = np.hstack([np.repeat(np.arange(n_classes), step), np.repeat(n_classes - 1, n_samples - step * n_classes)]) if shuffle: X, y = util_shuffle(X, y, random_state=generator) return X, y def _shuffle(data, random_state=None): generator = check_random_state(random_state) n_rows, n_cols = data.shape row_idx = generator.permutation(n_rows) col_idx = generator.permutation(n_cols) result = data[row_idx][:, col_idx] return result, row_idx, col_idx @_deprecate_positional_args def make_biclusters(shape, n_clusters, *, noise=0.0, minval=10, maxval=100, shuffle=True, random_state=None): """Generate an array with constant block diagonal structure for biclustering. Read more in the :ref:`User Guide `. Parameters ---------- shape : iterable of shape (n_rows, n_cols) The shape of the result. n_clusters : int The number of biclusters. noise : float, default=0.0 The standard deviation of the gaussian noise. minval : int, default=10 Minimum value of a bicluster. maxval : int, default=100 Maximum value of a bicluster. shuffle : bool, default=True Shuffle the samples. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape `shape` The generated array. rows : ndarray of shape (n_clusters, X.shape[0]) The indicators for cluster membership of each row. cols : ndarray of shape (n_clusters, X.shape[1]) The indicators for cluster membership of each column. References ---------- .. [1] Dhillon, I. S. (2001, August). Co-clustering documents and words using bipartite spectral graph partitioning. In Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 269-274). ACM. See Also -------- make_checkerboard """ generator = check_random_state(random_state) n_rows, n_cols = shape consts = generator.uniform(minval, maxval, n_clusters) # row and column clusters of approximately equal sizes row_sizes = generator.multinomial(n_rows, np.repeat(1.0 / n_clusters, n_clusters)) col_sizes = generator.multinomial(n_cols, np.repeat(1.0 / n_clusters, n_clusters)) row_labels = np.hstack(list(np.repeat(val, rep) for val, rep in zip(range(n_clusters), row_sizes))) col_labels = np.hstack(list(np.repeat(val, rep) for val, rep in zip(range(n_clusters), col_sizes))) result = np.zeros(shape, dtype=np.float64) for i in range(n_clusters): selector = np.outer(row_labels == i, col_labels == i) result[selector] += consts[i] if noise > 0: result += generator.normal(scale=noise, size=result.shape) if shuffle: result, row_idx, col_idx = _shuffle(result, random_state) row_labels = row_labels[row_idx] col_labels = col_labels[col_idx] rows = np.vstack([row_labels == c for c in range(n_clusters)]) cols = np.vstack([col_labels == c for c in range(n_clusters)]) return result, rows, cols @_deprecate_positional_args def make_checkerboard(shape, n_clusters, *, noise=0.0, minval=10, maxval=100, shuffle=True, random_state=None): """Generate an array with block checkerboard structure for biclustering. Read more in the :ref:`User Guide `. Parameters ---------- shape : tuple of shape (n_rows, n_cols) The shape of the result. n_clusters : int or array-like or shape (n_row_clusters, n_column_clusters) The number of row and column clusters. noise : float, default=0.0 The standard deviation of the gaussian noise. minval : int, default=10 Minimum value of a bicluster. maxval : int, default=100 Maximum value of a bicluster. shuffle : bool, default=True Shuffle the samples. random_state : int, RandomState instance or None, default=None Determines random number generation for dataset creation. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Returns ------- X : ndarray of shape `shape` The generated array. rows : ndarray of shape (n_clusters, X.shape[0]) The indicators for cluster membership of each row. cols : ndarray of shape (n_clusters, X.shape[1]) The indicators for cluster membership of each column. References ---------- .. [1] Kluger, Y., Basri, R., Chang, J. T., & Gerstein, M. (2003). Spectral biclustering of microarray data: coclustering genes and conditions. Genome research, 13(4), 703-716. See Also -------- make_biclusters """ generator = check_random_state(random_state) if hasattr(n_clusters, "__len__"): n_row_clusters, n_col_clusters = n_clusters else: n_row_clusters = n_col_clusters = n_clusters # row and column clusters of approximately equal sizes n_rows, n_cols = shape row_sizes = generator.multinomial(n_rows, np.repeat(1.0 / n_row_clusters, n_row_clusters)) col_sizes = generator.multinomial(n_cols, np.repeat(1.0 / n_col_clusters, n_col_clusters)) row_labels = np.hstack(list(np.repeat(val, rep) for val, rep in zip(range(n_row_clusters), row_sizes))) col_labels = np.hstack(list(np.repeat(val, rep) for val, rep in zip(range(n_col_clusters), col_sizes))) result = np.zeros(shape, dtype=np.float64) for i in range(n_row_clusters): for j in range(n_col_clusters): selector = np.outer(row_labels == i, col_labels == j) result[selector] += generator.uniform(minval, maxval) if noise > 0: result += generator.normal(scale=noise, size=result.shape) if shuffle: result, row_idx, col_idx = _shuffle(result, random_state) row_labels = row_labels[row_idx] col_labels = col_labels[col_idx] rows = np.vstack([row_labels == label for label in range(n_row_clusters) for _ in range(n_col_clusters)]) cols = np.vstack([col_labels == label for _ in range(n_row_clusters) for label in range(n_col_clusters)]) return result, rows, cols