"""Spectral biclustering algorithms.""" # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause from abc import ABCMeta, abstractmethod from numbers import Integral import numpy as np from scipy.linalg import norm from scipy.sparse import dia_matrix, issparse from scipy.sparse.linalg import eigsh, svds from ..base import BaseEstimator, BiclusterMixin, _fit_context from ..utils import check_random_state, check_scalar from ..utils._param_validation import Interval, StrOptions from ..utils.extmath import make_nonnegative, randomized_svd, safe_sparse_dot from ..utils.validation import assert_all_finite, validate_data from ._kmeans import KMeans, MiniBatchKMeans __all__ = ["SpectralCoclustering", "SpectralBiclustering"] def _scale_normalize(X): """Normalize ``X`` by scaling rows and columns independently. Returns the normalized matrix and the row and column scaling factors. """ X = make_nonnegative(X) row_diag = np.asarray(1.0 / np.sqrt(X.sum(axis=1))).squeeze() col_diag = np.asarray(1.0 / np.sqrt(X.sum(axis=0))).squeeze() row_diag = np.where(np.isnan(row_diag), 0, row_diag) col_diag = np.where(np.isnan(col_diag), 0, col_diag) if issparse(X): n_rows, n_cols = X.shape r = dia_matrix((row_diag, [0]), shape=(n_rows, n_rows)) c = dia_matrix((col_diag, [0]), shape=(n_cols, n_cols)) an = r * X * c else: an = row_diag[:, np.newaxis] * X * col_diag return an, row_diag, col_diag def _bistochastic_normalize(X, max_iter=1000, tol=1e-5): """Normalize rows and columns of ``X`` simultaneously so that all rows sum to one constant and all columns sum to a different constant. """ # According to paper, this can also be done more efficiently with # deviation reduction and balancing algorithms. X = make_nonnegative(X) X_scaled = X for _ in range(max_iter): X_new, _, _ = _scale_normalize(X_scaled) if issparse(X): dist = norm(X_scaled.data - X.data) else: dist = norm(X_scaled - X_new) X_scaled = X_new if dist is not None and dist < tol: break return X_scaled def _log_normalize(X): """Normalize ``X`` according to Kluger's log-interactions scheme.""" X = make_nonnegative(X, min_value=1) if issparse(X): raise ValueError( "Cannot compute log of a sparse matrix," " because log(x) diverges to -infinity as x" " goes to 0." ) L = np.log(X) row_avg = L.mean(axis=1)[:, np.newaxis] col_avg = L.mean(axis=0) avg = L.mean() return L - row_avg - col_avg + avg class BaseSpectral(BiclusterMixin, BaseEstimator, metaclass=ABCMeta): """Base class for spectral biclustering.""" _parameter_constraints: dict = { "svd_method": [StrOptions({"randomized", "arpack"})], "n_svd_vecs": [Interval(Integral, 0, None, closed="left"), None], "mini_batch": ["boolean"], "init": [StrOptions({"k-means++", "random"}), np.ndarray], "n_init": [Interval(Integral, 1, None, closed="left")], "random_state": ["random_state"], } @abstractmethod def __init__( self, n_clusters=3, svd_method="randomized", n_svd_vecs=None, mini_batch=False, init="k-means++", n_init=10, random_state=None, ): self.n_clusters = n_clusters self.svd_method = svd_method self.n_svd_vecs = n_svd_vecs self.mini_batch = mini_batch self.init = init self.n_init = n_init self.random_state = random_state @abstractmethod def _check_parameters(self, n_samples): """Validate parameters depending on the input data.""" @_fit_context(prefer_skip_nested_validation=True) def fit(self, X, y=None): """Create a biclustering for X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object SpectralBiclustering instance. """ X = validate_data(self, X, accept_sparse="csr", dtype=np.float64) self._check_parameters(X.shape[0]) self._fit(X) return self def _svd(self, array, n_components, n_discard): """Returns first `n_components` left and right singular vectors u and v, discarding the first `n_discard`. """ if self.svd_method == "randomized": kwargs = {} if self.n_svd_vecs is not None: kwargs["n_oversamples"] = self.n_svd_vecs u, _, vt = randomized_svd( array, n_components, random_state=self.random_state, **kwargs ) elif self.svd_method == "arpack": u, _, vt = svds(array, k=n_components, ncv=self.n_svd_vecs) if np.any(np.isnan(vt)): # some eigenvalues of A * A.T are negative, causing # sqrt() to be np.nan. This causes some vectors in vt # to be np.nan. A = safe_sparse_dot(array.T, array) random_state = check_random_state(self.random_state) # initialize with [-1,1] as in ARPACK v0 = random_state.uniform(-1, 1, A.shape[0]) _, v = eigsh(A, ncv=self.n_svd_vecs, v0=v0) vt = v.T if np.any(np.isnan(u)): A = safe_sparse_dot(array, array.T) random_state = check_random_state(self.random_state) # initialize with [-1,1] as in ARPACK v0 = random_state.uniform(-1, 1, A.shape[0]) _, u = eigsh(A, ncv=self.n_svd_vecs, v0=v0) assert_all_finite(u) assert_all_finite(vt) u = u[:, n_discard:] vt = vt[n_discard:] return u, vt.T def _k_means(self, data, n_clusters): if self.mini_batch: model = MiniBatchKMeans( n_clusters, init=self.init, n_init=self.n_init, random_state=self.random_state, ) else: model = KMeans( n_clusters, init=self.init, n_init=self.n_init, random_state=self.random_state, ) model.fit(data) centroid = model.cluster_centers_ labels = model.labels_ return centroid, labels def __sklearn_tags__(self): tags = super().__sklearn_tags__() tags.input_tags.sparse = True return tags class SpectralCoclustering(BaseSpectral): """Spectral Co-Clustering algorithm (Dhillon, 2001). Clusters rows and columns of an array `X` to solve the relaxed normalized cut of the bipartite graph created from `X` as follows: the edge between row vertex `i` and column vertex `j` has weight `X[i, j]`. The resulting bicluster structure is block-diagonal, since each row and each column belongs to exactly one bicluster. Supports sparse matrices, as long as they are nonnegative. Read more in the :ref:`User Guide `. Parameters ---------- n_clusters : int, default=3 The number of biclusters to find. svd_method : {'randomized', 'arpack'}, default='randomized' Selects the algorithm for finding singular vectors. May be 'randomized' or 'arpack'. If 'randomized', use :func:`sklearn.utils.extmath.randomized_svd`, which may be faster for large matrices. If 'arpack', use :func:`scipy.sparse.linalg.svds`, which is more accurate, but possibly slower in some cases. n_svd_vecs : int, default=None Number of vectors to use in calculating the SVD. Corresponds to `ncv` when `svd_method=arpack` and `n_oversamples` when `svd_method` is 'randomized`. mini_batch : bool, default=False Whether to use mini-batch k-means, which is faster but may get different results. init : {'k-means++', 'random'}, or ndarray of shape \ (n_clusters, n_features), default='k-means++' Method for initialization of k-means algorithm; defaults to 'k-means++'. n_init : int, default=10 Number of random initializations that are tried with the k-means algorithm. If mini-batch k-means is used, the best initialization is chosen and the algorithm runs once. Otherwise, the algorithm is run for each initialization and the best solution chosen. random_state : int, RandomState instance, default=None Used for randomizing the singular value decomposition and the k-means initialization. Use an int to make the randomness deterministic. See :term:`Glossary `. Attributes ---------- rows_ : array-like of shape (n_row_clusters, n_rows) Results of the clustering. `rows[i, r]` is True if cluster `i` contains row `r`. Available only after calling ``fit``. columns_ : array-like of shape (n_column_clusters, n_columns) Results of the clustering, like `rows`. row_labels_ : array-like of shape (n_rows,) The bicluster label of each row. column_labels_ : array-like of shape (n_cols,) The bicluster label of each column. biclusters_ : tuple of two ndarrays The tuple contains the `rows_` and `columns_` arrays. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 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 -------- SpectralBiclustering : Partitions rows and columns under the assumption that the data has an underlying checkerboard structure. References ---------- * :doi:`Dhillon, Inderjit S, 2001. Co-clustering documents and words using bipartite spectral graph partitioning. <10.1145/502512.502550>` Examples -------- >>> from sklearn.cluster import SpectralCoclustering >>> import numpy as np >>> X = np.array([[1, 1], [2, 1], [1, 0], ... [4, 7], [3, 5], [3, 6]]) >>> clustering = SpectralCoclustering(n_clusters=2, random_state=0).fit(X) >>> clustering.row_labels_ #doctest: +SKIP array([0, 1, 1, 0, 0, 0], dtype=int32) >>> clustering.column_labels_ #doctest: +SKIP array([0, 0], dtype=int32) >>> clustering SpectralCoclustering(n_clusters=2, random_state=0) """ _parameter_constraints: dict = { **BaseSpectral._parameter_constraints, "n_clusters": [Interval(Integral, 1, None, closed="left")], } def __init__( self, n_clusters=3, *, svd_method="randomized", n_svd_vecs=None, mini_batch=False, init="k-means++", n_init=10, random_state=None, ): super().__init__( n_clusters, svd_method, n_svd_vecs, mini_batch, init, n_init, random_state ) def _check_parameters(self, n_samples): if self.n_clusters > n_samples: raise ValueError( f"n_clusters should be <= n_samples={n_samples}. Got" f" {self.n_clusters} instead." ) def _fit(self, X): normalized_data, row_diag, col_diag = _scale_normalize(X) n_sv = 1 + int(np.ceil(np.log2(self.n_clusters))) u, v = self._svd(normalized_data, n_sv, n_discard=1) z = np.vstack((row_diag[:, np.newaxis] * u, col_diag[:, np.newaxis] * v)) _, labels = self._k_means(z, self.n_clusters) n_rows = X.shape[0] self.row_labels_ = labels[:n_rows] self.column_labels_ = labels[n_rows:] self.rows_ = np.vstack([self.row_labels_ == c for c in range(self.n_clusters)]) self.columns_ = np.vstack( [self.column_labels_ == c for c in range(self.n_clusters)] ) class SpectralBiclustering(BaseSpectral): """Spectral biclustering (Kluger, 2003). Partitions rows and columns under the assumption that the data has an underlying checkerboard structure. For instance, if there are two row partitions and three column partitions, each row will belong to three biclusters, and each column will belong to two biclusters. The outer product of the corresponding row and column label vectors gives this checkerboard structure. Read more in the :ref:`User Guide `. Parameters ---------- n_clusters : int or tuple (n_row_clusters, n_column_clusters), default=3 The number of row and column clusters in the checkerboard structure. method : {'bistochastic', 'scale', 'log'}, default='bistochastic' Method of normalizing and converting singular vectors into biclusters. May be one of 'scale', 'bistochastic', or 'log'. The authors recommend using 'log'. If the data is sparse, however, log normalization will not work, which is why the default is 'bistochastic'. .. warning:: if `method='log'`, the data must not be sparse. n_components : int, default=6 Number of singular vectors to check. n_best : int, default=3 Number of best singular vectors to which to project the data for clustering. svd_method : {'randomized', 'arpack'}, default='randomized' Selects the algorithm for finding singular vectors. May be 'randomized' or 'arpack'. If 'randomized', uses :func:`~sklearn.utils.extmath.randomized_svd`, which may be faster for large matrices. If 'arpack', uses `scipy.sparse.linalg.svds`, which is more accurate, but possibly slower in some cases. n_svd_vecs : int, default=None Number of vectors to use in calculating the SVD. Corresponds to `ncv` when `svd_method=arpack` and `n_oversamples` when `svd_method` is 'randomized`. mini_batch : bool, default=False Whether to use mini-batch k-means, which is faster but may get different results. init : {'k-means++', 'random'} or ndarray of shape (n_clusters, n_features), \ default='k-means++' Method for initialization of k-means algorithm; defaults to 'k-means++'. n_init : int, default=10 Number of random initializations that are tried with the k-means algorithm. If mini-batch k-means is used, the best initialization is chosen and the algorithm runs once. Otherwise, the algorithm is run for each initialization and the best solution chosen. random_state : int, RandomState instance, default=None Used for randomizing the singular value decomposition and the k-means initialization. Use an int to make the randomness deterministic. See :term:`Glossary `. Attributes ---------- rows_ : array-like of shape (n_row_clusters, n_rows) Results of the clustering. `rows[i, r]` is True if cluster `i` contains row `r`. Available only after calling ``fit``. columns_ : array-like of shape (n_column_clusters, n_columns) Results of the clustering, like `rows`. row_labels_ : array-like of shape (n_rows,) Row partition labels. column_labels_ : array-like of shape (n_cols,) Column partition labels. biclusters_ : tuple of two ndarrays The tuple contains the `rows_` and `columns_` arrays. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 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 -------- SpectralCoclustering : Spectral Co-Clustering algorithm (Dhillon, 2001). References ---------- * :doi:`Kluger, Yuval, et. al., 2003. Spectral biclustering of microarray data: coclustering genes and conditions. <10.1101/gr.648603>` Examples -------- >>> from sklearn.cluster import SpectralBiclustering >>> import numpy as np >>> X = np.array([[1, 1], [2, 1], [1, 0], ... [4, 7], [3, 5], [3, 6]]) >>> clustering = SpectralBiclustering(n_clusters=2, random_state=0).fit(X) >>> clustering.row_labels_ array([1, 1, 1, 0, 0, 0], dtype=int32) >>> clustering.column_labels_ array([1, 0], dtype=int32) >>> clustering SpectralBiclustering(n_clusters=2, random_state=0) For a more detailed example, see :ref:`sphx_glr_auto_examples_bicluster_plot_spectral_biclustering.py` """ _parameter_constraints: dict = { **BaseSpectral._parameter_constraints, "n_clusters": [Interval(Integral, 1, None, closed="left"), tuple], "method": [StrOptions({"bistochastic", "scale", "log"})], "n_components": [Interval(Integral, 1, None, closed="left")], "n_best": [Interval(Integral, 1, None, closed="left")], } def __init__( self, n_clusters=3, *, method="bistochastic", n_components=6, n_best=3, svd_method="randomized", n_svd_vecs=None, mini_batch=False, init="k-means++", n_init=10, random_state=None, ): super().__init__( n_clusters, svd_method, n_svd_vecs, mini_batch, init, n_init, random_state ) self.method = method self.n_components = n_components self.n_best = n_best def _check_parameters(self, n_samples): if isinstance(self.n_clusters, Integral): if self.n_clusters > n_samples: raise ValueError( f"n_clusters should be <= n_samples={n_samples}. Got" f" {self.n_clusters} instead." ) else: # tuple try: n_row_clusters, n_column_clusters = self.n_clusters check_scalar( n_row_clusters, "n_row_clusters", target_type=Integral, min_val=1, max_val=n_samples, ) check_scalar( n_column_clusters, "n_column_clusters", target_type=Integral, min_val=1, max_val=n_samples, ) except (ValueError, TypeError) as e: raise ValueError( "Incorrect parameter n_clusters has value:" f" {self.n_clusters}. It should either be a single integer" " or an iterable with two integers:" " (n_row_clusters, n_column_clusters)" " And the values are should be in the" " range: (1, n_samples)" ) from e if self.n_best > self.n_components: raise ValueError( f"n_best={self.n_best} must be <= n_components={self.n_components}." ) def _fit(self, X): n_sv = self.n_components if self.method == "bistochastic": normalized_data = _bistochastic_normalize(X) n_sv += 1 elif self.method == "scale": normalized_data, _, _ = _scale_normalize(X) n_sv += 1 elif self.method == "log": normalized_data = _log_normalize(X) n_discard = 0 if self.method == "log" else 1 u, v = self._svd(normalized_data, n_sv, n_discard) ut = u.T vt = v.T try: n_row_clusters, n_col_clusters = self.n_clusters except TypeError: n_row_clusters = n_col_clusters = self.n_clusters best_ut = self._fit_best_piecewise(ut, self.n_best, n_row_clusters) best_vt = self._fit_best_piecewise(vt, self.n_best, n_col_clusters) self.row_labels_ = self._project_and_cluster(X, best_vt.T, n_row_clusters) self.column_labels_ = self._project_and_cluster(X.T, best_ut.T, n_col_clusters) self.rows_ = np.vstack( [ self.row_labels_ == label for label in range(n_row_clusters) for _ in range(n_col_clusters) ] ) self.columns_ = np.vstack( [ self.column_labels_ == label for _ in range(n_row_clusters) for label in range(n_col_clusters) ] ) def _fit_best_piecewise(self, vectors, n_best, n_clusters): """Find the ``n_best`` vectors that are best approximated by piecewise constant vectors. The piecewise vectors are found by k-means; the best is chosen according to Euclidean distance. """ def make_piecewise(v): centroid, labels = self._k_means(v.reshape(-1, 1), n_clusters) return centroid[labels].ravel() piecewise_vectors = np.apply_along_axis(make_piecewise, axis=1, arr=vectors) dists = np.apply_along_axis(norm, axis=1, arr=(vectors - piecewise_vectors)) result = vectors[np.argsort(dists)[:n_best]] return result def _project_and_cluster(self, data, vectors, n_clusters): """Project ``data`` to ``vectors`` and cluster the result.""" projected = safe_sparse_dot(data, vectors) _, labels = self._k_means(projected, n_clusters) return labels