Inzynierka/Lib/site-packages/sklearn/cluster/_bicluster.py

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2023-06-02 12:51:02 +02:00
"""Spectral biclustering algorithms."""
# Authors : Kemal Eren
# License: BSD 3 clause
from abc import ABCMeta, abstractmethod
import numpy as np
from numbers import Integral
from scipy.linalg import norm
from scipy.sparse import dia_matrix, issparse
from scipy.sparse.linalg import eigsh, svds
from . import KMeans, MiniBatchKMeans
from ..base import BaseEstimator, BiclusterMixin
from ..utils import check_random_state
from ..utils import check_scalar
from ..utils.extmath import make_nonnegative, randomized_svd, safe_sparse_dot
from ..utils.validation import assert_all_finite
from ..utils._param_validation import Interval, StrOptions
__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."""
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.
"""
self._validate_params()
X = self._validate_data(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 _more_tags(self):
return {
"_xfail_checks": {
"check_estimators_dtypes": "raises nan error",
"check_fit2d_1sample": "_scale_normalize fails",
"check_fit2d_1feature": "raises apply_along_axis error",
"check_estimator_sparse_data": "does not fail gracefully",
"check_methods_subset_invariance": "empty array passed inside",
"check_dont_overwrite_parameters": "empty array passed inside",
"check_fit2d_predict1d": "empty array passed inside",
}
}
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 <spectral_coclustering>`.
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 <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,)
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 <spectral_biclustering>`.
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 <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.
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([0, 1], dtype=int32)
>>> clustering
SpectralBiclustering(n_clusters=2, random_state=0)
"""
_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