509 lines
20 KiB
Python
509 lines
20 KiB
Python
|
"""Spectral biclustering algorithms.
|
||
|
|
|
||
|
|
Authors : Kemal Eren
|
||
|
|
License: BSD 3 clause
|
||
|
|
|
||
|
|
"""
|
||
|
|
from abc import ABCMeta, abstractmethod
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
|
||
|
|
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 ..externals import six
|
||
|
|
from ..utils import check_random_state
|
||
|
|
|
||
|
|
from ..utils.extmath import (make_nonnegative, randomized_svd,
|
||
|
|
safe_sparse_dot)
|
||
|
|
|
||
|
|
from ..utils.validation import assert_all_finite, check_array
|
||
|
|
|
||
|
|
|
||
|
|
__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
|
||
|
|
dist = None
|
||
|
|
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(six.with_metaclass(ABCMeta, BaseEstimator,
|
||
|
|
BiclusterMixin)):
|
||
|
|
"""Base class for spectral biclustering."""
|
||
|
|
|
||
|
|
@abstractmethod
|
||
|
|
def __init__(self, n_clusters=3, svd_method="randomized",
|
||
|
|
n_svd_vecs=None, mini_batch=False, init="k-means++",
|
||
|
|
n_init=10, n_jobs=1, 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.n_jobs = n_jobs
|
||
|
|
self.random_state = random_state
|
||
|
|
|
||
|
|
def _check_parameters(self):
|
||
|
|
legal_svd_methods = ('randomized', 'arpack')
|
||
|
|
if self.svd_method not in legal_svd_methods:
|
||
|
|
raise ValueError("Unknown SVD method: '{0}'. svd_method must be"
|
||
|
|
" one of {1}.".format(self.svd_method,
|
||
|
|
legal_svd_methods))
|
||
|
|
|
||
|
|
def fit(self, X, y=None):
|
||
|
|
"""Creates a biclustering for X.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like, shape (n_samples, n_features)
|
||
|
|
|
||
|
|
y : Ignored
|
||
|
|
|
||
|
|
"""
|
||
|
|
X = check_array(X, accept_sparse='csr', dtype=np.float64)
|
||
|
|
self._check_parameters()
|
||
|
|
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, n_jobs=self.n_jobs,
|
||
|
|
random_state=self.random_state)
|
||
|
|
model.fit(data)
|
||
|
|
centroid = model.cluster_centers_
|
||
|
|
labels = model.labels_
|
||
|
|
return centroid, labels
|
||
|
|
|
||
|
|
|
||
|
|
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 : integer, optional, default: 3
|
||
|
|
The number of biclusters to find.
|
||
|
|
|
||
|
|
svd_method : string, optional, 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, optional, 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, optional, default: False
|
||
|
|
Whether to use mini-batch k-means, which is faster but may get
|
||
|
|
different results.
|
||
|
|
|
||
|
|
init : {'k-means++', 'random' or an ndarray}
|
||
|
|
Method for initialization of k-means algorithm; defaults to
|
||
|
|
'k-means++'.
|
||
|
|
|
||
|
|
n_init : int, optional, 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, optional, default: 1
|
||
|
|
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.
|
||
|
|
|
||
|
|
If -1 all CPUs are used. If 1 is given, no parallel computing code is
|
||
|
|
used at all, which is useful for debugging. For n_jobs below -1,
|
||
|
|
(n_cpus + 1 + n_jobs) are used. Thus for n_jobs = -2, all CPUs but one
|
||
|
|
are used.
|
||
|
|
|
||
|
|
random_state : int, RandomState instance or None, optional, default: None
|
||
|
|
If int, random_state is the seed used by the random number generator;
|
||
|
|
If RandomState instance, random_state is the random number generator;
|
||
|
|
If None, the random number generator is the RandomState instance used
|
||
|
|
by `np.random`.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
rows_ : array-like, 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, shape (n_column_clusters, n_columns)
|
||
|
|
Results of the clustering, like `rows`.
|
||
|
|
|
||
|
|
row_labels_ : array-like, shape (n_rows,)
|
||
|
|
The bicluster label of each row.
|
||
|
|
|
||
|
|
column_labels_ : array-like, shape (n_cols,)
|
||
|
|
The bicluster label of each column.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
|
||
|
|
* Dhillon, Inderjit S, 2001. `Co-clustering documents and words using
|
||
|
|
bipartite spectral graph partitioning
|
||
|
|
<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.3011>`__.
|
||
|
|
|
||
|
|
"""
|
||
|
|
def __init__(self, n_clusters=3, svd_method='randomized',
|
||
|
|
n_svd_vecs=None, mini_batch=False, init='k-means++',
|
||
|
|
n_init=10, n_jobs=1, random_state=None):
|
||
|
|
super(SpectralCoclustering, self).__init__(n_clusters,
|
||
|
|
svd_method,
|
||
|
|
n_svd_vecs,
|
||
|
|
mini_batch,
|
||
|
|
init,
|
||
|
|
n_init,
|
||
|
|
n_jobs,
|
||
|
|
random_state)
|
||
|
|
|
||
|
|
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 : integer or tuple (n_row_clusters, n_column_clusters)
|
||
|
|
The number of row and column clusters in the checkerboard
|
||
|
|
structure.
|
||
|
|
|
||
|
|
method : string, optional, 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'. CAUTION: if `method='log'`, the
|
||
|
|
data must not be sparse.
|
||
|
|
|
||
|
|
n_components : integer, optional, default: 6
|
||
|
|
Number of singular vectors to check.
|
||
|
|
|
||
|
|
n_best : integer, optional, default: 3
|
||
|
|
Number of best singular vectors to which to project the data
|
||
|
|
for clustering.
|
||
|
|
|
||
|
|
svd_method : string, optional, default: 'randomized'
|
||
|
|
Selects the algorithm for finding singular vectors. May be
|
||
|
|
'randomized' or 'arpack'. If 'randomized', uses
|
||
|
|
`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, optional, 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, optional, default: False
|
||
|
|
Whether to use mini-batch k-means, which is faster but may get
|
||
|
|
different results.
|
||
|
|
|
||
|
|
init : {'k-means++', 'random' or an ndarray}
|
||
|
|
Method for initialization of k-means algorithm; defaults to
|
||
|
|
'k-means++'.
|
||
|
|
|
||
|
|
n_init : int, optional, 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, optional, default: 1
|
||
|
|
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.
|
||
|
|
|
||
|
|
If -1 all CPUs are used. If 1 is given, no parallel computing code is
|
||
|
|
used at all, which is useful for debugging. For n_jobs below -1,
|
||
|
|
(n_cpus + 1 + n_jobs) are used. Thus for n_jobs = -2, all CPUs but one
|
||
|
|
are used.
|
||
|
|
|
||
|
|
random_state : int, RandomState instance or None, optional, default: None
|
||
|
|
If int, random_state is the seed used by the random number generator;
|
||
|
|
If RandomState instance, random_state is the random number generator;
|
||
|
|
If None, the random number generator is the RandomState instance used
|
||
|
|
by `np.random`.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
rows_ : array-like, 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, shape (n_column_clusters, n_columns)
|
||
|
|
Results of the clustering, like `rows`.
|
||
|
|
|
||
|
|
row_labels_ : array-like, shape (n_rows,)
|
||
|
|
Row partition labels.
|
||
|
|
|
||
|
|
column_labels_ : array-like, shape (n_cols,)
|
||
|
|
Column partition labels.
|
||
|
|
|
||
|
|
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>`__.
|
||
|
|
|
||
|
|
"""
|
||
|
|
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=1, random_state=None):
|
||
|
|
super(SpectralBiclustering, self).__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(SpectralBiclustering, self)._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
|