# Source code for sklearn.cluster.birch

# Authors: Manoj Kumar <manojkumarsivaraj334@gmail.com>
#          Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
#          Joel Nothman <joel.nothman@gmail.com>
from __future__ import division

import warnings
import numpy as np
from scipy import sparse
from math import sqrt

from ..metrics.pairwise import euclidean_distances
from ..base import TransformerMixin, ClusterMixin, BaseEstimator
from ..externals.six.moves import xrange
from ..utils import check_array
from ..utils.extmath import row_norms, safe_sparse_dot
from ..utils.validation import check_is_fitted
from ..exceptions import NotFittedError
from .hierarchical import AgglomerativeClustering

def _iterate_sparse_X(X):
"""This little hack returns a densified row when iterating over a sparse
matrix, instead of constructing a sparse matrix for every row that is
expensive.
"""
n_samples = X.shape
X_indices = X.indices
X_data = X.data
X_indptr = X.indptr

for i in xrange(n_samples):
row = np.zeros(X.shape)
startptr, endptr = X_indptr[i], X_indptr[i + 1]
nonzero_indices = X_indices[startptr:endptr]
row[nonzero_indices] = X_data[startptr:endptr]
yield row

def _split_node(node, threshold, branching_factor):
"""The node has to be split if there is no place for a new subcluster
in the node.
1. Two empty nodes and two empty subclusters are initialized.
2. The pair of distant subclusters are found.
3. The properties of the empty subclusters and nodes are updated
according to the nearest distance between the subclusters to the
pair of distant subclusters.
4. The two nodes are set as children to the two subclusters.
"""
new_subcluster1 = _CFSubcluster()
new_subcluster2 = _CFSubcluster()
new_node1 = _CFNode(
threshold, branching_factor, is_leaf=node.is_leaf,
n_features=node.n_features)
new_node2 = _CFNode(
threshold, branching_factor, is_leaf=node.is_leaf,
n_features=node.n_features)
new_subcluster1.child_ = new_node1
new_subcluster2.child_ = new_node2

if node.is_leaf:
if node.prev_leaf_ is not None:
node.prev_leaf_.next_leaf_ = new_node1
new_node1.prev_leaf_ = node.prev_leaf_
new_node1.next_leaf_ = new_node2
new_node2.prev_leaf_ = new_node1
new_node2.next_leaf_ = node.next_leaf_
if node.next_leaf_ is not None:
node.next_leaf_.prev_leaf_ = new_node2

dist = euclidean_distances(
node.centroids_, Y_norm_squared=node.squared_norm_, squared=True)
n_clusters = dist.shape

farthest_idx = np.unravel_index(
dist.argmax(), (n_clusters, n_clusters))
node1_dist, node2_dist = dist[[farthest_idx]]

node1_closer = node1_dist < node2_dist
for idx, subcluster in enumerate(node.subclusters_):
if node1_closer[idx]:
new_node1.append_subcluster(subcluster)
new_subcluster1.update(subcluster)
else:
new_node2.append_subcluster(subcluster)
new_subcluster2.update(subcluster)
return new_subcluster1, new_subcluster2

class _CFNode(object):
"""Each node in a CFTree is called a CFNode.

The CFNode can have a maximum of branching_factor
number of CFSubclusters.

Parameters
----------
threshold : float
Threshold needed for a new subcluster to enter a CFSubcluster.

branching_factor : int
Maximum number of CF subclusters in each node.

is_leaf : bool
We need to know if the CFNode is a leaf or not, in order to
retrieve the final subclusters.

n_features : int
The number of features.

Attributes
----------
subclusters_ : array-like
list of subclusters for a particular CFNode.

prev_leaf_ : _CFNode
prev_leaf. Useful only if is_leaf is True.

next_leaf_ : _CFNode
next_leaf. Useful only if is_leaf is True.
the final subclusters.

init_centroids_ : ndarray, shape (branching_factor + 1, n_features)
manipulate init_centroids_ throughout rather than centroids_ since
the centroids are just a view of the init_centroids_ .

init_sq_norm_ : ndarray, shape (branching_factor + 1,)
manipulate init_sq_norm_ throughout. similar to init_centroids_.

centroids_ : ndarray
view of init_centroids_.

squared_norm_ : ndarray
view of init_sq_norm_.

"""
def __init__(self, threshold, branching_factor, is_leaf, n_features):
self.threshold = threshold
self.branching_factor = branching_factor
self.is_leaf = is_leaf
self.n_features = n_features

# The list of subclusters, centroids and squared norms
# to manipulate throughout.
self.subclusters_ = []
self.init_centroids_ = np.zeros((branching_factor + 1, n_features))
self.init_sq_norm_ = np.zeros((branching_factor + 1))
self.squared_norm_ = []
self.prev_leaf_ = None
self.next_leaf_ = None

def append_subcluster(self, subcluster):
n_samples = len(self.subclusters_)
self.subclusters_.append(subcluster)
self.init_centroids_[n_samples] = subcluster.centroid_
self.init_sq_norm_[n_samples] = subcluster.sq_norm_

# Keep centroids and squared norm as views. In this way
# if we change init_centroids and init_sq_norm_, it is
# sufficient,
self.centroids_ = self.init_centroids_[:n_samples + 1, :]
self.squared_norm_ = self.init_sq_norm_[:n_samples + 1]

def update_split_subclusters(self, subcluster,
new_subcluster1, new_subcluster2):
"""Remove a subcluster from a node and update it with the
split subclusters.
"""
ind = self.subclusters_.index(subcluster)
self.subclusters_[ind] = new_subcluster1
self.init_centroids_[ind] = new_subcluster1.centroid_
self.init_sq_norm_[ind] = new_subcluster1.sq_norm_
self.append_subcluster(new_subcluster2)

def insert_cf_subcluster(self, subcluster):
"""Insert a new subcluster into the node."""
if not self.subclusters_:
self.append_subcluster(subcluster)
return False

threshold = self.threshold
branching_factor = self.branching_factor
# We need to find the closest subcluster among all the
# subclusters so that we can insert our new subcluster.
dist_matrix = np.dot(self.centroids_, subcluster.centroid_)
dist_matrix *= -2.
dist_matrix += self.squared_norm_
closest_index = np.argmin(dist_matrix)
closest_subcluster = self.subclusters_[closest_index]

# If the subcluster has a child, we need a recursive strategy.
if closest_subcluster.child_ is not None:
split_child = closest_subcluster.child_.insert_cf_subcluster(
subcluster)

if not split_child:
# If it is determined that the child need not be split, we
# can just update the closest_subcluster
closest_subcluster.update(subcluster)
self.init_centroids_[closest_index] = \
self.subclusters_[closest_index].centroid_
self.init_sq_norm_[closest_index] = \
self.subclusters_[closest_index].sq_norm_
return False

# things not too good. we need to redistribute the subclusters in
# our child node, and add a new subcluster in the parent
# subcluster to accommodate the new child.
else:
new_subcluster1, new_subcluster2 = _split_node(
closest_subcluster.child_, threshold, branching_factor)
self.update_split_subclusters(
closest_subcluster, new_subcluster1, new_subcluster2)

if len(self.subclusters_) > self.branching_factor:
return True
return False

# good to go!
else:
merged = closest_subcluster.merge_subcluster(
subcluster, self.threshold)
if merged:
self.init_centroids_[closest_index] = \
closest_subcluster.centroid_
self.init_sq_norm_[closest_index] = \
closest_subcluster.sq_norm_
return False

# not close to any other subclusters, and we still
elif len(self.subclusters_) < self.branching_factor:
self.append_subcluster(subcluster)
return False

# We do not have enough space nor is it closer to an
# other subcluster. We need to split.
else:
self.append_subcluster(subcluster)
return True

class _CFSubcluster(object):
"""Each subcluster in a CFNode is called a CFSubcluster.

A CFSubcluster can have a CFNode has its child.

Parameters
----------
linear_sum : ndarray, shape (n_features,), optional
Sample. This is kept optional to allow initialization of empty
subclusters.

Attributes
----------
n_samples_ : int
Number of samples that belong to each subcluster.

linear_sum_ : ndarray
Linear sum of all the samples in a subcluster. Prevents holding
all sample data in memory.

squared_sum_ : float
Sum of the squared l2 norms of all samples belonging to a subcluster.

centroid_ : ndarray
Centroid of the subcluster. Prevent recomputing of centroids when
CFNode.centroids_ is called.

child_ : _CFNode
Child Node of the subcluster. Once a given _CFNode is set as the child
of the _CFNode, it is set to self.child_.

sq_norm_ : ndarray
Squared norm of the subcluster. Used to prevent recomputing when
pairwise minimum distances are computed.
"""
def __init__(self, linear_sum=None):
if linear_sum is None:
self.n_samples_ = 0
self.squared_sum_ = 0.0
self.linear_sum_ = 0
else:
self.n_samples_ = 1
self.centroid_ = self.linear_sum_ = linear_sum
self.squared_sum_ = self.sq_norm_ = np.dot(
self.linear_sum_, self.linear_sum_)
self.child_ = None

def update(self, subcluster):
self.n_samples_ += subcluster.n_samples_
self.linear_sum_ += subcluster.linear_sum_
self.squared_sum_ += subcluster.squared_sum_
self.centroid_ = self.linear_sum_ / self.n_samples_
self.sq_norm_ = np.dot(self.centroid_, self.centroid_)

def merge_subcluster(self, nominee_cluster, threshold):
"""Check if a cluster is worthy enough to be merged. If
yes then merge.
"""
new_ss = self.squared_sum_ + nominee_cluster.squared_sum_
new_ls = self.linear_sum_ + nominee_cluster.linear_sum_
new_n = self.n_samples_ + nominee_cluster.n_samples_
new_centroid = (1 / new_n) * new_ls
new_norm = np.dot(new_centroid, new_centroid)
dot_product = (-2 * new_n) * new_norm
sq_radius = (new_ss + dot_product) / new_n + new_norm
if sq_radius <= threshold ** 2:
(self.n_samples_, self.linear_sum_, self.squared_sum_,
self.centroid_, self.sq_norm_) = \
new_n, new_ls, new_ss, new_centroid, new_norm
return True
return False

@property
dot_product = -2 * np.dot(self.linear_sum_, self.centroid_)
return sqrt(
((self.squared_sum_ + dot_product) / self.n_samples_) +
self.sq_norm_)

class Birch(BaseEstimator, TransformerMixin, ClusterMixin):
"""Implements the Birch clustering algorithm.

It is a memory-efficient, online-learning algorithm provided as an
alternative to :class:MiniBatchKMeans. It constructs a tree
data structure with the cluster centroids being read off the leaf.
These can be either the final cluster centroids or can be provided as input
to another clustering algorithm such as :class:AgglomerativeClustering.

Read more in the :ref:User Guide <birch>.

Parameters
----------
threshold : float, default 0.5
The radius of the subcluster obtained by merging a new sample and the
closest subcluster should be lesser than the threshold. Otherwise a new
subcluster is started. Setting this value to be very low promotes
splitting and vice-versa.

branching_factor : int, default 50
Maximum number of CF subclusters in each node. If a new samples enters
such that the number of subclusters exceed the branching_factor then
that node is split into two nodes with the subclusters redistributed
in each. The parent subcluster of that node is removed and two new
subclusters are added as parents of the 2 split nodes.

n_clusters : int, instance of sklearn.cluster model, default 3
Number of clusters after the final clustering step, which treats the
subclusters from the leaves as new samples.

- None : the final clustering step is not performed and the
subclusters are returned as they are.

- sklearn.cluster Estimator : If a model is provided, the model is
fit treating the subclusters as new samples and the initial data is
mapped to the label of the closest subcluster.

- int : the model fit is :class:AgglomerativeClustering with
n_clusters set to be equal to the int.

compute_labels : bool, default True
Whether or not to compute labels for each fit.

copy : bool, default True
Whether or not to make a copy of the given data. If set to False,
the initial data will be overwritten.

Attributes
----------
root_ : _CFNode
Root of the CFTree.

dummy_leaf_ : _CFNode
Start pointer to all the leaves.

subcluster_centers_ : ndarray,
Centroids of all subclusters read directly from the leaves.

subcluster_labels_ : ndarray,
Labels assigned to the centroids of the subclusters after
they are clustered globally.

labels_ : ndarray, shape (n_samples,)
Array of labels assigned to the input data.
if partial_fit is used instead of fit, they are assigned to the
last batch of data.

Examples
--------
>>> from sklearn.cluster import Birch
>>> X = [[0, 1], [0.3, 1], [-0.3, 1], [0, -1], [0.3, -1], [-0.3, -1]]
>>> brc = Birch(branching_factor=50, n_clusters=None, threshold=0.5,
... compute_labels=True)
>>> brc.fit(X)
Birch(branching_factor=50, compute_labels=True, copy=True, n_clusters=None,
threshold=0.5)
>>> brc.predict(X)
array([0, 0, 0, 1, 1, 1])

References
----------
* Tian Zhang, Raghu Ramakrishnan, Maron Livny
BIRCH: An efficient data clustering method for large databases.
http://www.cs.sfu.ca/CourseCentral/459/han/papers/zhang96.pdf

* Roberto Perdisci
JBirch - Java implementation of BIRCH clustering algorithm

Notes
-----
The tree data structure consists of nodes with each node consisting of
a number of subclusters. The maximum number of subclusters in a node
is determined by the branching factor. Each subcluster maintains a
linear sum, squared sum and the number of samples in that subcluster.
In addition, each subcluster can also have a node as its child, if the
subcluster is not a member of a leaf node.

For a new point entering the root, it is merged with the subcluster closest
to it and the linear sum, squared sum and the number of samples of that
subcluster are updated. This is done recursively till the properties of
the leaf node are updated.
"""

def __init__(self, threshold=0.5, branching_factor=50, n_clusters=3,
compute_labels=True, copy=True):
self.threshold = threshold
self.branching_factor = branching_factor
self.n_clusters = n_clusters
self.compute_labels = compute_labels
self.copy = copy

[docs]    def fit(self, X, y=None):
"""
Build a CF Tree for the input data.

Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Input data.

y : Ignored

"""
self.fit_, self.partial_fit_ = True, False
return self._fit(X)

def _fit(self, X):
X = check_array(X, accept_sparse='csr', copy=self.copy)
threshold = self.threshold
branching_factor = self.branching_factor

if branching_factor <= 1:
raise ValueError("Branching_factor should be greater than one.")
n_samples, n_features = X.shape

# If partial_fit is called for the first time or fit is called, we
# start a new tree.
partial_fit = getattr(self, 'partial_fit_')
has_root = getattr(self, 'root_', None)
if getattr(self, 'fit_') or (partial_fit and not has_root):
# The first root is the leaf. Manipulate this object throughout.
self.root_ = _CFNode(threshold, branching_factor, is_leaf=True,
n_features=n_features)

# To enable getting back subclusters.
self.dummy_leaf_ = _CFNode(threshold, branching_factor,
is_leaf=True, n_features=n_features)
self.dummy_leaf_.next_leaf_ = self.root_
self.root_.prev_leaf_ = self.dummy_leaf_

# Cannot vectorize. Enough to convince to use cython.
if not sparse.issparse(X):
iter_func = iter
else:
iter_func = _iterate_sparse_X

for sample in iter_func(X):
subcluster = _CFSubcluster(linear_sum=sample)
split = self.root_.insert_cf_subcluster(subcluster)

if split:
new_subcluster1, new_subcluster2 = _split_node(
self.root_, threshold, branching_factor)
del self.root_
self.root_ = _CFNode(threshold, branching_factor,
is_leaf=False,
n_features=n_features)
self.root_.append_subcluster(new_subcluster1)
self.root_.append_subcluster(new_subcluster2)

centroids = np.concatenate([
leaf.centroids_ for leaf in self._get_leaves()])
self.subcluster_centers_ = centroids

self._global_clustering(X)
return self

def _get_leaves(self):
"""
Retrieve the leaves of the CF Node.

Returns
-------
leaves : array-like
List of the leaf nodes.
"""
leaf_ptr = self.dummy_leaf_.next_leaf_
leaves = []
while leaf_ptr is not None:
leaves.append(leaf_ptr)
leaf_ptr = leaf_ptr.next_leaf_
return leaves

[docs]    def partial_fit(self, X=None, y=None):
"""
Online learning. Prevents rebuilding of CFTree from scratch.

Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features), None
Input data. If X is not provided, only the global clustering
step is done.

y : Ignored

"""
self.partial_fit_, self.fit_ = True, False
if X is None:
# Perform just the final global clustering step.
self._global_clustering()
return self
else:
self._check_fit(X)
return self._fit(X)

def _check_fit(self, X):
is_fitted = hasattr(self, 'subcluster_centers_')

# Called by partial_fit, before fitting.
has_partial_fit = hasattr(self, 'partial_fit_')

# Should raise an error if one does not fit before predicting.
if not (is_fitted or has_partial_fit):
raise NotFittedError("Fit training data before predicting")

if is_fitted and X.shape != self.subcluster_centers_.shape:
raise ValueError(
"Training data and predicted data do "
"not have same number of features.")

[docs]    def predict(self, X):
"""
Predict data using the centroids_ of subclusters.

Avoid computation of the row norms of X.

Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Input data.

Returns
-------
labels : ndarray, shape(n_samples)
Labelled data.
"""
X = check_array(X, accept_sparse='csr')
self._check_fit(X)
reduced_distance = safe_sparse_dot(X, self.subcluster_centers_.T)
reduced_distance *= -2
reduced_distance += self._subcluster_norms
return self.subcluster_labels_[np.argmin(reduced_distance, axis=1)]

[docs]    def transform(self, X):
"""
Transform X into subcluster centroids dimension.

Each dimension represents the distance from the sample point to each
cluster centroid.

Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Input data.

Returns
-------
X_trans : {array-like, sparse matrix}, shape (n_samples, n_clusters)
Transformed data.
"""
check_is_fitted(self, 'subcluster_centers_')
return euclidean_distances(X, self.subcluster_centers_)

def _global_clustering(self, X=None):
"""
Global clustering for the subclusters obtained after fitting
"""
clusterer = self.n_clusters
centroids = self.subcluster_centers_
compute_labels = (X is not None) and self.compute_labels

# Preprocessing for the global clustering.
not_enough_centroids = False
if isinstance(clusterer, int):
clusterer = AgglomerativeClustering(
n_clusters=self.n_clusters)
# There is no need to perform the global clustering step.
if len(centroids) < self.n_clusters:
not_enough_centroids = True
elif (clusterer is not None and not
hasattr(clusterer, 'fit_predict')):
raise ValueError("n_clusters should be an instance of "
"ClusterMixin or an int")

# To use in predict to avoid recalculation.
self._subcluster_norms = row_norms(
self.subcluster_centers_, squared=True)

if clusterer is None or not_enough_centroids:
self.subcluster_labels_ = np.arange(len(centroids))
if not_enough_centroids:
warnings.warn(
"Number of subclusters found (%d) by Birch is less "
"than (%d). Decrease the threshold."
% (len(centroids), self.n_clusters))
else:
# The global clustering step that clusters the subclusters of
# the leaves. It assumes the centroids of the subclusters as
# samples and finds the final centroids.
self.subcluster_labels_ = clusterer.fit_predict(
self.subcluster_centers_)

if compute_labels:
self.labels_ = self.predict(X)