_birch.py

# Authors: Manoj Kumar <manojkumarsivaraj334@gmail.com>
#          Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
#          Joel Nothman <joel.nothman@gmail.com>
# License: BSD 3 clause

import warnings
from math import sqrt
from numbers import Integral, Real

import numpy as np
from scipy import sparse

from .._config import config_context
from ..base import (
    BaseEstimator,
    ClassNamePrefixFeaturesOutMixin,
    ClusterMixin,
    TransformerMixin,
    _fit_context,
)
from ..exceptions import ConvergenceWarning
from ..metrics import pairwise_distances_argmin
from ..metrics.pairwise import euclidean_distances
from ..utils._param_validation import Interval
from ..utils.extmath import row_norms
from ..utils.validation import check_is_fitted
from . 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[0]
    X_indices = X.indices
    X_data = X.data
    X_indptr = X.indptr

    for i in range(n_samples):
        row = np.zeros(X.shape[1])
        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=threshold,
        branching_factor=branching_factor,
        is_leaf=node.is_leaf,
        n_features=node.n_features,
        dtype=node.init_centroids_.dtype,
    )
    new_node2 = _CFNode(
        threshold=threshold,
        branching_factor=branching_factor,
        is_leaf=node.is_leaf,
        n_features=node.n_features,
        dtype=node.init_centroids_.dtype,
    )
    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[0]

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

    node1_closer = node1_dist < node2_dist
    # make sure node1 is closest to itself even if all distances are equal.
    # This can only happen when all node.centroids_ are duplicates leading to all
    # distances between centroids being zero.
    node1_closer[farthest_idx[0]] = True

    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:
    """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_ : list
        List of subclusters for a particular CFNode.

    prev_leaf_ : _CFNode
        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 of 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 of shape (branching_factor + 1,)
        manipulate init_sq_norm_ throughout. similar to ``init_centroids_``.

    centroids_ : ndarray of shape (branching_factor + 1, n_features)
        View of ``init_centroids_``.

    squared_norm_ : ndarray of shape (branching_factor + 1,)
        View of ``init_sq_norm_``.

    """

    def __init__(self, *, threshold, branching_factor, is_leaf, n_features, dtype):
        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), dtype=dtype)
        self.init_sq_norm_ = np.zeros((branching_factor + 1), dtype)
        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 *= -2.0
        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
            # have space, so add.
            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:
    """Each subcluster in a CFNode is called a CFSubcluster.

    A CFSubcluster can have a CFNode has its child.

    Parameters
    ----------
    linear_sum : ndarray of shape (n_features,), default=None
        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 of shape (branching_factor + 1, n_features)
        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 of shape (branching_factor + 1,)
        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.centroid_ = 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_sq_norm = np.dot(new_centroid, new_centroid)

        # The squared radius of the cluster is defined:
        #   r^2  = sum_i ||x_i - c||^2 / n
        # with x_i the n points assigned to the cluster and c its centroid:
        #   c = sum_i x_i / n
        # This can be expanded to:
        #   r^2 = sum_i ||x_i||^2 / n - 2 < sum_i x_i / n, c> + n ||c||^2 / n
        # and therefore simplifies to:
        #   r^2 = sum_i ||x_i||^2 / n - ||c||^2
        sq_radius = new_ss / new_n - new_sq_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_sq_norm)
            return True
        return False

    @property
    def radius(self):
        """Return radius of the subcluster"""
        # Because of numerical issues, this could become negative
        sq_radius = self.squared_sum_ / self.n_samples_ - self.sq_norm_
        return sqrt(max(0, sq_radius))


class Birch(
    ClassNamePrefixFeaturesOutMixin, ClusterMixin, TransformerMixin, BaseEstimator
):
    """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>`.

    .. versionadded:: 0.16

    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 or None, 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.

        - :mod:`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 of 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.

    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
    --------
    MiniBatchKMeans : Alternative implementation that does incremental updates
        of the centers' positions using mini-batches.

    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.

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

    * Roberto Perdisci
      JBirch - Java implementation of BIRCH clustering algorithm
      https://code.google.com/archive/p/jbirch

    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(n_clusters=None)
    >>> brc.fit(X)
    Birch(n_clusters=None)
    >>> brc.predict(X)
    array([0, 0, 0, 1, 1, 1])
    """

    _parameter_constraints: dict = {
        "threshold": [Interval(Real, 0.0, None, closed="neither")],
        "branching_factor": [Interval(Integral, 1, None, closed="neither")],
        "n_clusters": [None, ClusterMixin, Interval(Integral, 1, None, closed="left")],
        "compute_labels": ["boolean"],
        "copy": ["boolean"],
    }

    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

    @_fit_context(prefer_skip_nested_validation=True)
    def fit(self, X, y=None):
        """
        Build a CF Tree for the input data.

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

        y : Ignored
            Not used, present here for API consistency by convention.

        Returns
        -------
        self
            Fitted estimator.
        """
        return self._fit(X, partial=False)

    def _fit(self, X, partial):
        has_root = getattr(self, "root_", None)
        first_call = not (partial and has_root)

        X = self._validate_data(
            X,
            accept_sparse="csr",
            copy=self.copy,
            reset=first_call,
            dtype=[np.float64, np.float32],
        )
        threshold = self.threshold
        branching_factor = self.branching_factor

        n_samples, n_features = X.shape

        # If partial_fit is called for the first time or fit is called, we
        # start a new tree.
        if first_call:
            # The first root is the leaf. Manipulate this object throughout.
            self.root_ = _CFNode(
                threshold=threshold,
                branching_factor=branching_factor,
                is_leaf=True,
                n_features=n_features,
                dtype=X.dtype,
            )

            # To enable getting back subclusters.
            self.dummy_leaf_ = _CFNode(
                threshold=threshold,
                branching_factor=branching_factor,
                is_leaf=True,
                n_features=n_features,
                dtype=X.dtype,
            )
            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=threshold,
                    branching_factor=branching_factor,
                    is_leaf=False,
                    n_features=n_features,
                    dtype=X.dtype,
                )
                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._n_features_out = self.subcluster_centers_.shape[0]

        self._global_clustering(X)
        return self

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

        Returns
        -------
        leaves : list of shape (n_leaves,)
            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

    @_fit_context(prefer_skip_nested_validation=True)
    def partial_fit(self, X=None, y=None):
        """
        Online learning. Prevents rebuilding of CFTree from scratch.

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

        y : Ignored
            Not used, present here for API consistency by convention.

        Returns
        -------
        self
            Fitted estimator.
        """
        if X is None:
            # Perform just the final global clustering step.
            self._global_clustering()
            return self
        else:
            return self._fit(X, partial=True)

    def _check_fit(self, X):
        check_is_fitted(self)

        if (
            hasattr(self, "subcluster_centers_")
            and X.shape[1] != self.subcluster_centers_.shape[1]
        ):
            raise ValueError(
                "Training data and predicted data do not have same number of features."
            )

    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} of shape (n_samples, n_features)
            Input data.

        Returns
        -------
        labels : ndarray of shape(n_samples,)
            Labelled data.
        """
        check_is_fitted(self)
        X = self._validate_data(X, accept_sparse="csr", reset=False)
        return self._predict(X)

    def _predict(self, X):
        """Predict data using the ``centroids_`` of subclusters."""
        kwargs = {"Y_norm_squared": self._subcluster_norms}

        with config_context(assume_finite=True):
            argmin = pairwise_distances_argmin(
                X, self.subcluster_centers_, metric_kwargs=kwargs
            )
        return self.subcluster_labels_[argmin]

    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} of shape (n_samples, n_features)
            Input data.

        Returns
        -------
        X_trans : {array-like, sparse matrix} of shape (n_samples, n_clusters)
            Transformed data.
        """
        check_is_fitted(self)
        X = self._validate_data(X, accept_sparse="csr", reset=False)
        with config_context(assume_finite=True):
            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, Integral):
            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

        # 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),
                    ConvergenceWarning,
                )
        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)

    def _more_tags(self):
        return {"preserves_dtype": [np.float64, np.float32]}