def score(self, X, y=None):
"""Opposite of the value of X on the K-means objective.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
New data.
Returns
-------
score : float
Opposite of the value of X on the K-means objective.
"""
check_is_fitted(self, 'cluster_centers_')
X = self._check_test_data(X)
x_squared_norms = row_norms(X, squared=True)
return -_labels_inertia(X, x_squared_norms, self.cluster_centers_)[1]
def predict(self, X):
"""Predict the closest cluster each sample in X belongs to.
In the vector quantization literature, `cluster_centers_` is called
the code book and each value returned by `predict` is the index of
the closest code in the code book.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
New data to predict.
Returns
-------
labels : array, shape [n_samples,]
Index of the cluster each sample belongs to.
"""
check_is_fitted(self, 'cluster_centers_')
X = self._check_test_data(X)
x_squared_norms = row_norms(X, squared=True)
return _labels_inertia(X, x_squared_norms, self.cluster_centers_)[0]
def normalize(X, norm='l2', axis=1, copy=True, return_norm=False):
"""Scale input vectors individually to unit norm (vector length).
Read more in the :ref:`User Guide <preprocessing_normalization>`.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data to normalize, element by element.
scipy.sparse matrices should be in CSR format to avoid an
un-necessary copy.
norm : 'l1', 'l2', or 'max', optional ('l2' by default)
The norm to use to normalize each non zero sample (or each non-zero
feature if axis is 0).
axis : 0 or 1, optional (1 by default)
axis used to normalize the data along. If 1, independently normalize
each sample, otherwise (if 0) normalize each feature.
copy : boolean, optional, default True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSR matrix and if axis is 1).
return_norm : boolean, default False
whether to return the computed norms
Returns
-------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
Normalized input X.
norms : array, shape [n_samples] if axis=1 else [n_features]
An array of norms along given axis for X.
When X is sparse, a NotImplementedError will be raised
for norm 'l1' or 'l2'.
See also
--------
Normalizer: Performs normalization using the ``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
Notes
-----
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
if norm not in ('l1', 'l2', 'max'):
raise ValueError("'%s' is not a supported norm" % norm)
if axis == 0:
sparse_format = 'csc'
elif axis == 1:
sparse_format = 'csr'
else:
raise ValueError("'%d' is not a supported axis" % axis)
X = check_array(X, sparse_format, copy=copy,
estimator='the normalize function', dtype=FLOAT_DTYPES)
if axis == 0:
X = X.T
if sparse.issparse(X):
if return_norm and norm in ('l1', 'l2'):
raise NotImplementedError("return_norm=True is not implemented "
"for sparse matrices with norm 'l1' "
"or norm 'l2'")
if norm == 'l1':
inplace_csr_row_normalize_l1(X)
elif norm == 'l2':
inplace_csr_row_normalize_l2(X)
elif norm == 'max':
_, norms = min_max_axis(X, 1)
norms_elementwise = norms.repeat(np.diff(X.indptr))
mask = norms_elementwise != 0
X.data[mask] /= norms_elementwise[mask]
else:
if norm == 'l1':
norms = np.abs(X).sum(axis=1)
elif norm == 'l2':
norms = row_norms(X)
elif norm == 'max':
norms = np.max(X, axis=1)
norms = _handle_zeros_in_scale(norms, copy=False)
X /= norms[:, np.newaxis]
if axis == 0:
X = X.T
if return_norm:
return X, norms
else:
return X
def euclidean_distances(X,
Y=None,
Y_norm_squared=None,
squared=False,
X_norm_squared=None):
"""
Considering the rows of X (and Y=X) as vectors, compute the
distance matrix between each pair of vectors.
For efficiency reasons, the euclidean distance between a pair of row
vector x and y is computed as::
dist(x, y) = sqrt(dot(x, x) - 2 * dot(x, y) + dot(y, y))
This formulation has two advantages over other ways of computing distances.
First, it is computationally efficient when dealing with sparse data.
Second, if one argument varies but the other remains unchanged, then
`dot(x, x)` and/or `dot(y, y)` can be pre-computed.
However, this is not the most precise way of doing this computation, and
the distance matrix returned by this function may not be exactly
symmetric as required by, e.g., ``scipy.spatial.distance`` functions.
Read more in the :ref:`User Guide <metrics>`.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples_1, n_features)
Y : {array-like, sparse matrix}, shape (n_samples_2, n_features)
Y_norm_squared : array-like, shape (n_samples_2, ), optional
Pre-computed dot-products of vectors in Y (e.g.,
``(Y**2).sum(axis=1)``)
squared : boolean, optional
Return squared Euclidean distances.
X_norm_squared : array-like, shape = [n_samples_1], optional
Pre-computed dot-products of vectors in X (e.g.,
``(X**2).sum(axis=1)``)
Returns
-------
distances : {array, sparse matrix}, shape (n_samples_1, n_samples_2)
Examples
--------
>>> from sklearn.metrics.pairwise import euclidean_distances
>>> X = [[0, 1], [1, 1]]
>>> # distance between rows of X
>>> euclidean_distances(X, X)
array([[ 0., 1.],
[ 1., 0.]])
>>> # get distance to origin
>>> euclidean_distances(X, [[0, 0]])
array([[ 1. ],
[ 1.41421356]])
See also
--------
paired_distances : distances betweens pairs of elements of X and Y.
"""
X, Y = check_pairwise_arrays(X, Y)
if X_norm_squared is not None:
XX = check_array(X_norm_squared)
if XX.shape == (1, X.shape[0]):
XX = XX.T
elif XX.shape != (X.shape[0], 1):
raise ValueError(
"Incompatible dimensions for X and X_norm_squared")
else:
XX = row_norms(X, squared=True)[:, np.newaxis]
if X is Y: # shortcut in the common case euclidean_distances(X, X)
YY = XX.T
elif Y_norm_squared is not None:
YY = np.atleast_2d(Y_norm_squared)
if YY.shape != (1, Y.shape[0]):
raise ValueError(
"Incompatible dimensions for Y and Y_norm_squared")
else:
YY = row_norms(Y, squared=True)[np.newaxis, :]
distances = safe_sparse_dot(X, Y.T, dense_output=True)
distances *= -2
distances += XX
distances += YY
np.maximum(distances, 0, out=distances)
if X is Y:
# Ensure that distances between vectors and themselves are set to 0.0.
# This may not be the case due to floating point rounding errors.
distances.flat[::distances.shape[0] + 1] = 0.0
return distances if squared else np.sqrt(distances, out=distances)
def pairwise_distances_argmin_min(X,
Y,
axis=1,
metric="euclidean",
batch_size=500,
metric_kwargs=None):
"""Compute minimum distances between one point and a set of points.
This function computes for each row in X, the index of the row of Y which
is closest (according to the specified distance). The minimal distances are
also returned.
This is mostly equivalent to calling:
(pairwise_distances(X, Y=Y, metric=metric).argmin(axis=axis),
pairwise_distances(X, Y=Y, metric=metric).min(axis=axis))
but uses much less memory, and is faster for large arrays.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples1, n_features)
Array containing points.
Y : {array-like, sparse matrix}, shape (n_samples2, n_features)
Arrays containing points.
axis : int, optional, default 1
Axis along which the argmin and distances are to be computed.
metric : string or callable, default 'euclidean'
metric to use for distance computation. Any metric from scikit-learn
or scipy.spatial.distance can be used.
If metric is a callable function, it is called on each
pair of instances (rows) and the resulting value recorded. The callable
should take two arrays as input and return one value indicating the
distance between them. This works for Scipy's metrics, but is less
efficient than passing the metric name as a string.
Distance matrices are not supported.
Valid values for metric are:
- from scikit-learn: ['cityblock', 'cosine', 'euclidean', 'l1', 'l2',
'manhattan']
- from scipy.spatial.distance: ['braycurtis', 'canberra', 'chebyshev',
'correlation', 'dice', 'hamming', 'jaccard', 'kulsinski',
'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto',
'russellrao', 'seuclidean', 'sokalmichener', 'sokalsneath',
'sqeuclidean', 'yule']
See the documentation for scipy.spatial.distance for details on these
metrics.
batch_size : integer
To reduce memory consumption over the naive solution, data are
processed in batches, comprising batch_size rows of X and
batch_size rows of Y. The default value is quite conservative, but
can be changed for fine-tuning. The larger the number, the larger the
memory usage.
metric_kwargs : dict, optional
Keyword arguments to pass to specified metric function.
Returns
-------
argmin : numpy.ndarray
Y[argmin[i], :] is the row in Y that is closest to X[i, :].
distances : numpy.ndarray
distances[i] is the distance between the i-th row in X and the
argmin[i]-th row in Y.
See also
--------
sklearn.metrics.pairwise_distances
sklearn.metrics.pairwise_distances_argmin
"""
dist_func = None
if metric in PAIRWISE_DISTANCE_FUNCTIONS:
dist_func = PAIRWISE_DISTANCE_FUNCTIONS[metric]
elif not callable(metric) and not isinstance(metric, str):
raise ValueError("'metric' must be a string or a callable")
X, Y = check_pairwise_arrays(X, Y)
if metric_kwargs is None:
metric_kwargs = {}
if axis == 0:
X, Y = Y, X
# Allocate output arrays
indices = np.empty(X.shape[0], dtype=np.intp)
values = np.empty(X.shape[0])
values.fill(np.infty)
for chunk_x in gen_batches(X.shape[0], batch_size):
X_chunk = X[chunk_x, :]
for chunk_y in gen_batches(Y.shape[0], batch_size):
Y_chunk = Y[chunk_y, :]
if dist_func is not None:
if metric == 'euclidean': # special case, for speed
d_chunk = safe_sparse_dot(X_chunk,
Y_chunk.T,
dense_output=True)
d_chunk *= -2
d_chunk += row_norms(X_chunk, squared=True)[:, np.newaxis]
d_chunk += row_norms(Y_chunk, squared=True)[np.newaxis, :]
np.maximum(d_chunk, 0, d_chunk)
else:
d_chunk = dist_func(X_chunk, Y_chunk, **metric_kwargs)
else:
d_chunk = pairwise_distances(X_chunk,
Y_chunk,
metric=metric,
**metric_kwargs)
# Update indices and minimum values using chunk
min_indices = d_chunk.argmin(axis=1)
min_values = d_chunk[np.arange(chunk_x.stop - chunk_x.start),
min_indices]
flags = values[chunk_x] > min_values
indices[chunk_x][flags] = min_indices[flags] + chunk_y.start
values[chunk_x][flags] = min_values[flags]
if metric == "euclidean" and not metric_kwargs.get("squared", False):
np.sqrt(values, values)
return indices, values
def _init_centroids(X,
k,
init,
random_state=None,
x_squared_norms=None,
init_size=None):
"""Compute the initial centroids
Parameters
----------
X : array, shape (n_samples, n_features)
k : int
number of centroids
init : {'k-means++', 'random' or ndarray or callable} optional
Method for initialization
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`.
x_squared_norms : array, shape (n_samples,), optional
Squared euclidean norm of each data point. Pass it if you have it at
hands already to avoid it being recomputed here. Default: None
init_size : int, optional
Number of samples to randomly sample for speeding up the
initialization (sometimes at the expense of accuracy): the
only algorithm is initialized by running a batch KMeans on a
random subset of the data. This needs to be larger than k.
Returns
-------
centers : array, shape(k, n_features)
"""
random_state = check_random_state(random_state)
n_samples = X.shape[0]
if x_squared_norms is None:
x_squared_norms = row_norms(X, squared=True)
if init_size is not None and init_size < n_samples:
if init_size < k:
warnings.warn("init_size=%d should be larger than k=%d. "
"Setting it to 3*k" % (init_size, k),
RuntimeWarning,
stacklevel=2)
init_size = 3 * k
init_indices = random_state.randint(0, n_samples, init_size)
X = X[init_indices]
x_squared_norms = x_squared_norms[init_indices]
n_samples = X.shape[0]
elif n_samples < k:
raise ValueError("n_samples=%d should be larger than k=%d" %
(n_samples, k))
if isinstance(init, string_types) and init == 'k-means++':
centers = _k_init(X,
k,
random_state=random_state,
x_squared_norms=x_squared_norms)
elif isinstance(init, string_types) and init == 'random':
seeds = random_state.permutation(n_samples)[:k]
centers = X[seeds]
elif hasattr(init, '__array__'):
# ensure that the centers have the same dtype as X
# this is a requirement of fused types of cython
centers = np.array(init, dtype=X.dtype)
elif callable(init):
centers = init(X, k, random_state=random_state)
centers = np.asarray(centers, dtype=X.dtype)
else:
raise ValueError("the init parameter for the k-means should "
"be 'k-means++' or 'random' or an ndarray, "
"'%s' (type '%s') was passed." % (init, type(init)))
if sp.issparse(centers):
centers = centers.toarray()
_validate_center_shape(X, k, centers)
return centers