547 lines
21 KiB
Python
547 lines
21 KiB
Python
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"""Spectral biclustering algorithms."""
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# Authors : Kemal Eren
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# License: BSD 3 clause
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from abc import ABCMeta, abstractmethod
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import warnings
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import numpy as np
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from scipy.linalg import norm
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from scipy.sparse import dia_matrix, issparse
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from scipy.sparse.linalg import eigsh, svds
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from . import KMeans, MiniBatchKMeans
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from ..base import BaseEstimator, BiclusterMixin
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from ..utils import check_random_state
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from ..utils.extmath import (make_nonnegative, randomized_svd,
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safe_sparse_dot)
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from ..utils.validation import assert_all_finite, _deprecate_positional_args
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__all__ = ['SpectralCoclustering',
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'SpectralBiclustering']
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def _scale_normalize(X):
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"""Normalize ``X`` by scaling rows and columns independently.
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Returns the normalized matrix and the row and column scaling
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factors.
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"""
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X = make_nonnegative(X)
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row_diag = np.asarray(1.0 / np.sqrt(X.sum(axis=1))).squeeze()
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col_diag = np.asarray(1.0 / np.sqrt(X.sum(axis=0))).squeeze()
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row_diag = np.where(np.isnan(row_diag), 0, row_diag)
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col_diag = np.where(np.isnan(col_diag), 0, col_diag)
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if issparse(X):
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n_rows, n_cols = X.shape
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r = dia_matrix((row_diag, [0]), shape=(n_rows, n_rows))
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c = dia_matrix((col_diag, [0]), shape=(n_cols, n_cols))
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an = r * X * c
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else:
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an = row_diag[:, np.newaxis] * X * col_diag
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return an, row_diag, col_diag
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def _bistochastic_normalize(X, max_iter=1000, tol=1e-5):
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"""Normalize rows and columns of ``X`` simultaneously so that all
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rows sum to one constant and all columns sum to a different
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constant.
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"""
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# According to paper, this can also be done more efficiently with
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# deviation reduction and balancing algorithms.
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X = make_nonnegative(X)
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X_scaled = X
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for _ in range(max_iter):
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X_new, _, _ = _scale_normalize(X_scaled)
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if issparse(X):
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dist = norm(X_scaled.data - X.data)
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else:
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dist = norm(X_scaled - X_new)
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X_scaled = X_new
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if dist is not None and dist < tol:
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break
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return X_scaled
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def _log_normalize(X):
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"""Normalize ``X`` according to Kluger's log-interactions scheme."""
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X = make_nonnegative(X, min_value=1)
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if issparse(X):
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raise ValueError("Cannot compute log of a sparse matrix,"
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" because log(x) diverges to -infinity as x"
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" goes to 0.")
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L = np.log(X)
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row_avg = L.mean(axis=1)[:, np.newaxis]
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col_avg = L.mean(axis=0)
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avg = L.mean()
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return L - row_avg - col_avg + avg
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class BaseSpectral(BiclusterMixin, BaseEstimator, metaclass=ABCMeta):
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"""Base class for spectral biclustering."""
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@abstractmethod
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def __init__(self, n_clusters=3, svd_method="randomized",
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n_svd_vecs=None, mini_batch=False, init="k-means++",
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n_init=10, n_jobs='deprecated', random_state=None):
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self.n_clusters = n_clusters
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self.svd_method = svd_method
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self.n_svd_vecs = n_svd_vecs
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self.mini_batch = mini_batch
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self.init = init
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self.n_init = n_init
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self.n_jobs = n_jobs
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self.random_state = random_state
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def _check_parameters(self):
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legal_svd_methods = ('randomized', 'arpack')
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if self.svd_method not in legal_svd_methods:
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raise ValueError("Unknown SVD method: '{0}'. svd_method must be"
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" one of {1}.".format(self.svd_method,
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legal_svd_methods))
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def fit(self, X, y=None):
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"""Creates a biclustering for X.
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Parameters
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----------
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X : array-like, shape (n_samples, n_features)
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y : Ignored
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"""
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if self.n_jobs != 'deprecated':
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warnings.warn("'n_jobs' was deprecated in version 0.23 and will be"
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" removed in 0.25.", FutureWarning)
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X = self._validate_data(X, accept_sparse='csr', dtype=np.float64)
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self._check_parameters()
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self._fit(X)
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return self
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def _svd(self, array, n_components, n_discard):
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"""Returns first `n_components` left and right singular
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vectors u and v, discarding the first `n_discard`.
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"""
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if self.svd_method == 'randomized':
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kwargs = {}
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if self.n_svd_vecs is not None:
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kwargs['n_oversamples'] = self.n_svd_vecs
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u, _, vt = randomized_svd(array, n_components,
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random_state=self.random_state,
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**kwargs)
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elif self.svd_method == 'arpack':
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u, _, vt = svds(array, k=n_components, ncv=self.n_svd_vecs)
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if np.any(np.isnan(vt)):
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# some eigenvalues of A * A.T are negative, causing
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# sqrt() to be np.nan. This causes some vectors in vt
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# to be np.nan.
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A = safe_sparse_dot(array.T, array)
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random_state = check_random_state(self.random_state)
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# initialize with [-1,1] as in ARPACK
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v0 = random_state.uniform(-1, 1, A.shape[0])
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_, v = eigsh(A, ncv=self.n_svd_vecs, v0=v0)
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vt = v.T
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if np.any(np.isnan(u)):
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A = safe_sparse_dot(array, array.T)
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random_state = check_random_state(self.random_state)
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# initialize with [-1,1] as in ARPACK
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v0 = random_state.uniform(-1, 1, A.shape[0])
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_, u = eigsh(A, ncv=self.n_svd_vecs, v0=v0)
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assert_all_finite(u)
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assert_all_finite(vt)
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u = u[:, n_discard:]
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vt = vt[n_discard:]
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return u, vt.T
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def _k_means(self, data, n_clusters):
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if self.mini_batch:
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model = MiniBatchKMeans(n_clusters,
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init=self.init,
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n_init=self.n_init,
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random_state=self.random_state)
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else:
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model = KMeans(n_clusters, init=self.init,
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n_init=self.n_init, n_jobs=self.n_jobs,
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random_state=self.random_state)
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model.fit(data)
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centroid = model.cluster_centers_
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labels = model.labels_
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return centroid, labels
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class SpectralCoclustering(BaseSpectral):
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"""Spectral Co-Clustering algorithm (Dhillon, 2001).
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Clusters rows and columns of an array `X` to solve the relaxed
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normalized cut of the bipartite graph created from `X` as follows:
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the edge between row vertex `i` and column vertex `j` has weight
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`X[i, j]`.
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The resulting bicluster structure is block-diagonal, since each
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row and each column belongs to exactly one bicluster.
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Supports sparse matrices, as long as they are nonnegative.
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Read more in the :ref:`User Guide <spectral_coclustering>`.
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Parameters
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----------
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n_clusters : int, default=3
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The number of biclusters to find.
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svd_method : {'randomized', 'arpack'}, default='randomized'
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Selects the algorithm for finding singular vectors. May be
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'randomized' or 'arpack'. If 'randomized', use
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:func:`sklearn.utils.extmath.randomized_svd`, which may be faster
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for large matrices. If 'arpack', use
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:func:`scipy.sparse.linalg.svds`, which is more accurate, but
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possibly slower in some cases.
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n_svd_vecs : int, default=None
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Number of vectors to use in calculating the SVD. Corresponds
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to `ncv` when `svd_method=arpack` and `n_oversamples` when
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`svd_method` is 'randomized`.
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mini_batch : bool, default=False
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Whether to use mini-batch k-means, which is faster but may get
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different results.
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init : {'k-means++', 'random', or ndarray of shape \
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(n_clusters, n_features), default='k-means++'
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Method for initialization of k-means algorithm; defaults to
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'k-means++'.
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n_init : int, default=10
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Number of random initializations that are tried with the
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k-means algorithm.
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If mini-batch k-means is used, the best initialization is
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chosen and the algorithm runs once. Otherwise, the algorithm
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is run for each initialization and the best solution chosen.
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n_jobs : int, default=None
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The number of jobs to use for the computation. This works by breaking
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down the pairwise matrix into n_jobs even slices and computing them in
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parallel.
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``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
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``-1`` means using all processors. See :term:`Glossary <n_jobs>`
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for more details.
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.. deprecated:: 0.23
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``n_jobs`` was deprecated in version 0.23 and will be removed in
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0.25.
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random_state : int, RandomState instance, default=None
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Used for randomizing the singular value decomposition and the k-means
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initialization. Use an int to make the randomness deterministic.
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See :term:`Glossary <random_state>`.
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Attributes
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----------
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rows_ : array-like of shape (n_row_clusters, n_rows)
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Results of the clustering. `rows[i, r]` is True if
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cluster `i` contains row `r`. Available only after calling ``fit``.
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columns_ : array-like of shape (n_column_clusters, n_columns)
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Results of the clustering, like `rows`.
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row_labels_ : array-like of shape (n_rows,)
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The bicluster label of each row.
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column_labels_ : array-like of shape (n_cols,)
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The bicluster label of each column.
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Examples
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--------
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>>> from sklearn.cluster import SpectralCoclustering
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>>> import numpy as np
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>>> X = np.array([[1, 1], [2, 1], [1, 0],
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... [4, 7], [3, 5], [3, 6]])
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>>> clustering = SpectralCoclustering(n_clusters=2, random_state=0).fit(X)
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>>> clustering.row_labels_ #doctest: +SKIP
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array([0, 1, 1, 0, 0, 0], dtype=int32)
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>>> clustering.column_labels_ #doctest: +SKIP
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array([0, 0], dtype=int32)
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>>> clustering
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SpectralCoclustering(n_clusters=2, random_state=0)
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References
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----------
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* Dhillon, Inderjit S, 2001. `Co-clustering documents and words using
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bipartite spectral graph partitioning
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<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.3011>`__.
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"""
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@_deprecate_positional_args
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def __init__(self, n_clusters=3, *, svd_method='randomized',
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n_svd_vecs=None, mini_batch=False, init='k-means++',
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n_init=10, n_jobs='deprecated', random_state=None):
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super().__init__(n_clusters,
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svd_method,
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n_svd_vecs,
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mini_batch,
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init,
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n_init,
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n_jobs,
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random_state)
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def _fit(self, X):
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normalized_data, row_diag, col_diag = _scale_normalize(X)
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n_sv = 1 + int(np.ceil(np.log2(self.n_clusters)))
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u, v = self._svd(normalized_data, n_sv, n_discard=1)
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z = np.vstack((row_diag[:, np.newaxis] * u,
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col_diag[:, np.newaxis] * v))
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_, labels = self._k_means(z, self.n_clusters)
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n_rows = X.shape[0]
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self.row_labels_ = labels[:n_rows]
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self.column_labels_ = labels[n_rows:]
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self.rows_ = np.vstack([self.row_labels_ == c
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for c in range(self.n_clusters)])
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self.columns_ = np.vstack([self.column_labels_ == c
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for c in range(self.n_clusters)])
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class SpectralBiclustering(BaseSpectral):
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"""Spectral biclustering (Kluger, 2003).
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Partitions rows and columns under the assumption that the data has
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an underlying checkerboard structure. For instance, if there are
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two row partitions and three column partitions, each row will
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belong to three biclusters, and each column will belong to two
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biclusters. The outer product of the corresponding row and column
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label vectors gives this checkerboard structure.
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Read more in the :ref:`User Guide <spectral_biclustering>`.
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Parameters
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----------
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n_clusters : int or tuple (n_row_clusters, n_column_clusters), default=3
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The number of row and column clusters in the checkerboard
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structure.
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method : {'bistochastic', 'scale', 'log'}, default='bistochastic'
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Method of normalizing and converting singular vectors into
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biclusters. May be one of 'scale', 'bistochastic', or 'log'.
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The authors recommend using 'log'. If the data is sparse,
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however, log normalization will not work, which is why the
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default is 'bistochastic'.
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.. warning::
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if `method='log'`, the data must be sparse.
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n_components : int, default=6
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Number of singular vectors to check.
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n_best : int, default=3
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Number of best singular vectors to which to project the data
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for clustering.
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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 (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.
|
||
|
|
|
||
|
|
n_jobs : int, default=None
|
||
|
|
The number of jobs to use for the computation. This works by breaking
|
||
|
|
down the pairwise matrix into n_jobs even slices and computing them in
|
||
|
|
parallel.
|
||
|
|
|
||
|
|
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
|
||
|
|
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
|
||
|
|
for more details.
|
||
|
|
|
||
|
|
.. deprecated:: 0.23
|
||
|
|
``n_jobs`` was deprecated in version 0.23 and will be removed in
|
||
|
|
0.25.
|
||
|
|
|
||
|
|
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 <random_state>`.
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
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([0, 1], dtype=int32)
|
||
|
|
>>> clustering
|
||
|
|
SpectralBiclustering(n_clusters=2, random_state=0)
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
|
||
|
|
* Kluger, Yuval, et. al., 2003. `Spectral biclustering of microarray
|
||
|
|
data: coclustering genes and conditions
|
||
|
|
<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.135.1608>`__.
|
||
|
|
|
||
|
|
"""
|
||
|
|
@_deprecate_positional_args
|
||
|
|
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, n_jobs='deprecated', random_state=None):
|
||
|
|
super().__init__(n_clusters,
|
||
|
|
svd_method,
|
||
|
|
n_svd_vecs,
|
||
|
|
mini_batch,
|
||
|
|
init,
|
||
|
|
n_init,
|
||
|
|
n_jobs,
|
||
|
|
random_state)
|
||
|
|
self.method = method
|
||
|
|
self.n_components = n_components
|
||
|
|
self.n_best = n_best
|
||
|
|
|
||
|
|
def _check_parameters(self):
|
||
|
|
super()._check_parameters()
|
||
|
|
legal_methods = ('bistochastic', 'scale', 'log')
|
||
|
|
if self.method not in legal_methods:
|
||
|
|
raise ValueError("Unknown method: '{0}'. method must be"
|
||
|
|
" one of {1}.".format(self.method, legal_methods))
|
||
|
|
try:
|
||
|
|
int(self.n_clusters)
|
||
|
|
except TypeError:
|
||
|
|
try:
|
||
|
|
r, c = self.n_clusters
|
||
|
|
int(r)
|
||
|
|
int(c)
|
||
|
|
except (ValueError, TypeError):
|
||
|
|
raise ValueError("Incorrect parameter n_clusters has value:"
|
||
|
|
" {}. It should either be a single integer"
|
||
|
|
" or an iterable with two integers:"
|
||
|
|
" (n_row_clusters, n_column_clusters)")
|
||
|
|
if self.n_components < 1:
|
||
|
|
raise ValueError("Parameter n_components must be greater than 0,"
|
||
|
|
" but its value is {}".format(self.n_components))
|
||
|
|
if self.n_best < 1:
|
||
|
|
raise ValueError("Parameter n_best must be greater than 0,"
|
||
|
|
" but its value is {}".format(self.n_best))
|
||
|
|
if self.n_best > self.n_components:
|
||
|
|
raise ValueError("n_best cannot be larger than"
|
||
|
|
" n_components, but {} > {}"
|
||
|
|
"".format(self.n_best, 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
|